C (gcc), 174 bytes

char c[99];j;k;
#define F(x)atoi(x)*atoi(x)*atoi(x)
main(int a,char**v){strcpy(c,v[1]);while(k++-2)strcpy(c+(j+=strlen(v[k])),v[k+1]);exit(atoi(c)!=F(v[1])+F(v[2])+F(v[3]));}

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APL(NARS), 15 chars

{(∊⍕¨⍵)≡⍕+/⍵*3}

test:

  {(∊⍕¨⍵)≡⍕+/⍵*3}10 0 0
1
~
  {(∊⍕¨⍵)≡⍕+/⍵*3}10 0 1
1
~
  {(∊⍕¨⍵)≡⍕+/⍵*3}¨(1 5 3)(2 2 13)(4 0 7)(828 538 472)
┌4───────┐
│ 1 1 1 1│
└~───────┘
  {(∊⍕¨⍵)≡⍕+/⍵*3}¨(1 2 3)(4 5 6)(6 0 0)(166 500 334)
┌4───────┐
│ 0 0 0 0│
└~───────┘

Jalapeño, 4 bytes

J=Σₓ³

Explained

J=Σₓ³
J      # Join (implicit input) together
 =     # Is equal to
  Σₓ   # The sum of (implicit input) mapped by
    ³  # Cubed

Hex-Dump of Bytecode

       0  1  2  3  4  5  6  7  8  9  A  B  C  D  E  F
0000: 14 59 ea 62                                     

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Desmos, 66 bytes

d(n)=10^{floor(log(n+0^n))+1}
f(a,b,c)=a^3+b^3+c^3-c-d(c)(b+d(b)a)

This solution evolved very close to Aiden Chow's solution, but it does improve it by one byte. 0 represents truthy outputs, any any other integer represents falsey.

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AWK, 24 bytes

$0=$1^3+$2^3+$3^3~$1$2$3

awk '$0=$1^3+$2^3+$3^3~$1$2$3' << "1 5 3"

Prints 1 if truthy, or nothing.

Husk, 8 bytes

=dṁd¹ṁ^3

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Takes a list of numbers and outputs 1 (truthy) "if the sum of their cubes is equal to the concatenation of those numbers", otherwise 0 (falsy).

Explanation:

     ṁ^3  # sum up the cubes
  ṁd¹     # split every number into its digits and flatten the list
 d        # join digits back into a single number
=         # check for the equality

Clojure, 56 bytes

#(=(seq(str(apply +(for[i %](* i i i)))))(mapcat str %))

TIO. This was surprisingly painless, thanks to str and mapcat. Takes the input as a list of numbers.

Excel, 23 Bytes

An anonymous workbook function that takes input from a vertical array at A1# and outputs to the calling cell

--(A1&A2&A3)=SUM(A1#^3)

Previous Version, 24 bytes

A slightly more elegant solution that uses the Concat builtin

--CONCAT(A1#)=SUM(A1#^3)

Sample Output

For the input array ={1;5;3} outputs the following

ARBLE, 21 bytes

a^3+b^3+c^3-(a..b..c)

0 for truthy, non-zero for falsey.

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Run all tests!

PowerShell Core, 45 bytes

-join$args-(($args|%{"$_*"*3+1})-join'+'|iex)

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Takes 3 integers as parameters
Returns \$0\$ for true, otherwise false=

Desmos, 81 67 bytes

-14 bytes thanks to @emanresu A due to the fact that I didn't realize that it was always guaranteed to be exactly 3 numerical inputs. I was originally solving for an arbitrary amount of numerical inputs.

c(x,y)=x10^{floor(log(y+0^y))+1}+y
f(x,y,z)=c(c(x,y),z)-x^3-y^3-z^3

Returns 0 for truthy and a non-zero integer for falsey.

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Try It On Desmos! - Prettified

AWK, 24 21 bytes

$1$2$3~$1^3+$2^3+$3^3

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Prints the digits if true, or returns nothing.

Japt, 5 bytes

x³¥U¬

Try it here

x³¥U¬     :Implicit input of array U
x         :Sum of
 ³        :  Cubes
  ¥       :Loosely equal to
   U¬     :  U joined to a string

Wolfram Language (Mathematica), 31 30 bytes

boring wins

s[#.#^2]==s/@#<>""&
s=ToString

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Go, 108 bytes

import."fmt"
func f(a,b,c int)bool{n:=0
Sscanf(Sprintf("%d%d%d",a,b,c),"%d",&n)
return a*a*a+b*b*b+c*c*c==n}

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MathGolf, 5 bytes

‼yⁿΣ=

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Explanation:

‼     # Apply the next two operands separately on the (implicit) input-triplet:
 y    #  Join them together
  ⁿ   #  Take the cube of each
   Σ  # Sum the triplet of cubes
    = # Check if the two lists are the same
      # (after which the entire stack joined together is output implicitly)

05AB1E, 6 bytes

3mOIJQ

Try it online or verify all test cases.

The 3m could alternatively be ** or n* for the same byte-count; or the order could be swapped to JI3mOQ as well:
Try it online.

Explanation:

3m      # Take the cube of each value in the (implicit) input-triplet
  O     # Sum those together
   I    # Push the input-triplet again
    J   # Join them together
     Q  # Check if the two are the same
        # (after which the result is output implicitly)

Python 3, 44 bytes

lambda x:sum(map(pow,x,[3]*3))-int(3*'%d'%x)

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-1 byte thanks to Jonathan Allan

-2 bytes thanks to xnor

Returns truthy (nonzero integers) for False cases and falsey (zero integers) for True cases.

Python 3, 45 bytes

lambda a,b,c:a**3+b**3+c**3-int(f'{a}{b}{c}')

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Javascript (V8), 40 bytes

a=>a.reduce((x,y)=>x+y**3,0)==a.join('')

where a is number[], so it should work for any number of arguments.

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33 bytes

Thanks @Neil and @tsh for the shorter version!

a=>a.map(x=>s-=x**3,s=a.join``)|s

JavaScript (Node.js), 31 bytes

(x,y,z)=>[x]+y+z-x**3-y**3-z**3

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A boring trivial solution is short...

Lua, 38 bytes

x,y,z=...print(x^3+y^3+z^3==0|x..y..z)

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Julia, 26 24 23 bytes

-n="$(n'n.^2)"==join(n)

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Thanks to ovs for -2 and further -1 by Ashlin Harris.

Java (JDK), 120 bytes

t->t.stream().mapToInt(x->x*x*x).sum()==Integer.parseInt(t.stream().map(Object::toString).collect(Collectors.joining()))

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I'm not sure if the import of java.util.List needs to be counted. The predicate takes a List and some old advice says that all the types for lambdas need to be included, with any imports, but in JShell it is imported by default and in JDK 23 (which is currently only a preview edition) you also get it for free in a Java program that is all in one file (you can even skip declaring a class or having a full public-static-void-main), but TIO doesn't support JShell or recent versions of Java.

Stack control 1.1, 6 characters

:³+⇆◡=

Explanation

:  - duplicates original array
³  - cubes every array element
+  - sum of array elements
⇆  - swap to another array
◡  - reversed concatenates values from array
=  - check if values are equals

gnuplot, 33 bytes

f(a,b,c)=a**3+b**3+c**3=="".a.b.c

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A function that inputs 3 integer values and outputs 1 if their sum of cubes is equal to the concatenation of those numbers, otherwise the output is 0.

J, 15 bytes

;(=1#.^&3)&:".>

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Takes input as list of boxed strings.

Bash, 28

Sometimes the simple solution is best:

(($1**3+$2**3+$3**3^$1$2$3))

This script takes a list as command-line parameters as input. e.g. ./cubeconcat.sh 1 5 3. It returns a shell exit code: 1 for True, 0 for False.

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Previous, overcomplicated solution:

Bash, 37

(($(eval printf %s +\$[$1**3] ^ $1)))

This script takes a single quoted brace-enclosed, comma-separated list as input. e.g. ./cubeconcat.sh "{1,5,3}". It returns a shell exit code: 1 for True, 0 for False.

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Bash, 33 bytes

[ $1$2$3 = $[$1**3+$2**3+$3**3] ]

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The script returns a shell exit code: 1 for True, 0 for False.

Charcoal, 9 bytes

⁼Ｉ⪫θωΣＸθ³

Try it online! Link is to verbose version of code. Takes input as an array and outputs a Charcoal boolean, i.e. - if the sum of cubes equals the concatenation, nothing if not. Explanation:

   θ        Input array
  ⪫         Joined by
    ω       Predefined variable empty string
 Ｉ          Cast to integer
⁼           Equals
       θ    Input array
      Ｘ     Vectorised raised to power
        ³   Literal integer `3`
     Σ      Take the sum
            Implicitly print

Retina, 54 bytes

,(\d+),(\d+)
$1$2,$.(***_$2*$2*$2*_$`*$`*$`*
^(.+),\1$

Try it online! Link includes test cases. Explanation:

,(\d+),(\d+)

Match the first number in $`, the second number in $1 and the third number in $2.

$1$2,$.(***_$2*$2*$2*_$`*$`*$`*

Concatenate the input numbers, then compute the sum of the cube of $1 (implicitly because it's the first number in the match), the cube of $2 and the cube of $`. (Retina 1 will do this calculation using arbitrary-precision integers as it knows it will be converting the result back to decimal.)

^(.+),\1$

Check that the two results are the same.

Pyth, 9 bytes

qsjkQsm**

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First time golfing in Pyth, so this might be not optimal.

Explanation:

sm** calculates the sum of the cubes;

jkQ joins the list elements into a string and s converts the result to a number;

q: are the values equal?

MATLAB, 41 bytes

f=@(x)sum(x.^3)==str2num(sprintf('%d',x))

An @-function that accepts input as column vector.

>> f([828;538;472])
ans =
  logical
  1
>> f([200;0;200])
ans =
  logical
  0

Brachylog, 7 bytes

^₃ᵐ+~c?

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Explanation

^₃ᵐ        Map cube on the input list
   +       The sum of these cubes…
    ~c?    …can be deconcatenated into the original input list

Ruby, 30 bytes

->a{a.sum{|x|x**3}.to_s==a*''}

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R, 30 29 bytes

Edit: -1 byte thanks to @Kirill L..

\(x)x^2%*%x==Reduce(paste0,x)

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Windows Batch, 43 bytes

cmd/cset/a%1*%1*%1+%2*%2*%2+%3*%3*%3-%1%2%3

Prints 0 for truthy, <>0 for falsy.

Sorry, no TIO available; save as C:\Temp\cg274690.cmd or whatever.cmd, run from cmd.exe or PowerShell:
C:\Temp\cg274690.cmd 1 5 3

Ungolfed:

cmd.exe /c set /a %1 * %1 * %1 + %2 * %2 * %2 + %3 * %3 * %3 - %1%2%3

This starts another instance of cmd.exe, as using set /a inside a batch script requires an assignment, which would then have to be echoed out, for a total of 49 bytes (using LF as EOL):

set/ax=%1*%1*%1+%2*%2*%2+%3*%3*%3-%1%2%3
echo %x%

set /a used interactively inside a cmd prompt (or passed with /c) prints the result directly.

C++, 186 165 146 bytes

#include<iostream>
using namespace std;int main(){int a,b,c;cin>>a>>b>>c;cout<<(a*a*a+b*b*b+c*c*c==stoi(to_string(a)+to_string(b)+to_string(c)));}

(-16 thanks to Mousetail) (-19 thanks to Blue)

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Red, 41 bytes

func[a][(sum a * a * a)= do rejoin to[]a]

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Takes input as a vector of three numbers. Vectors support arithmetic with multiple values at once, but not powers.

Explanation

func[a][         ; start function taking argument a
(sum a * a * a)  ; sum of cubes
=                ; does it equal...
to[]a            ; input converted to regular list
rejoin           ; concatenated to string
do               ; evaluated (converted to integer)
]                ; end function

Kotlin 52 Bytes

{it.map{it*it*it}.sum()-it.joinToString("").toInt()}

Accepts a List<Int> and outputs zero for true and a non-zero integer for false.

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Perl 5 -MList::Util=sum -ap, 27 bytes

$_=y/ //dr==sum map$_**3,@F

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Factor, ⁴⁶ 45 bytes

[ 4 dupn v* v. swap "%d%d%d"vsprintf dec> = ]

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Explanation

[                 ! start function
4 dupn            ! put 4 total copies of input list on stack
v*                ! multiply top two
v.                ! dot product w/ third
swap              ! put input on top
"%d%d%d"vsprintf  ! concat all three to string
dec>              ! to number
=                 ! check equality
]                 ! end function

Jelly,  5  4 bytes

-1 thanks to Unrelated String! (*3S {cube then sum} -> ḋ² {dot-product with squared values}.)

ḋ²⁼V

A monadic Link that accepts a list of non-negative integers (with or without any leading zeros^*) and yields 1 if the list concatenates to the sum of the cubes of its elements or 0 if not.

Try it online! Or see the test-suite.

How?

ḋ²⁼V - Link: list, A = [a, b, c]
 ²   - square {A} -> [a², b², c²]
ḋ    - {A} dot-product {that} -> a³+b³+c³
   V - evaluate {A} as Jelly code -> concatenated integer *
  ⁼  - {SumOfCubes} equals {that}?

^{* Leading zeros produce a side effect of printing zeros before yielding the result.}

Setanta, 84 66 bytes

gniomh(a,b,c){toradh a*a*a+b*b*b+c*c*c==go_uimh(nasc@[a,b,c](""))}

try-setanta.ie link

Arturo, 31 bytes

$->a->=do join a∑map a=>[&^3]

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Explanation

$->a->        ; a function taking a list named a
=             ; are the following two values equal?
do join a     ; concatenation of input as a number
∑             ; and sum of...
map a=>[&^3]  ; inputs cubed

Google Sheets, 31 bytes

=SUMPRODUCT(A:A^3)=--JOIN(,A:A) 

Haskell, 33 bytes

(==).show.sum.map(^3)<*>(>>=show)

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• sum.map(^3) is the sum of the cubes
• show.sum.map(^3) is stringifies the sum
• (>>=show) is concatMap show, i.e. concatenetes the numbers
• <*> feeds the input to both arguments

K (ngn/k), 17 bytes

{(,/$x)~$+/x*x*x}

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Uiua, 17 14 12 chars

-3 chars thanks to Chunes by replacing fork with on

-2 chars thanks to OVS because I missed the existance of a power operator

=/+ⁿ3⟜⍜°⋕/⍚⊂

Pad Link

Python 3, 36 bytes

lambda*I:eval(3*"%d"%I+3*"-%d**3"%I)

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eval golf of @Jitse's answer who generously declined to include it in their post. Returns zero for True and nonzero integer for False.

APL+WIN, 17 bytes

Prompts for integers.

(⍎∊⍕¨s)=+/(s←⎕)*3

Try it online! Thanks to Dyalog Classic

JavaScript (Node.js), 32 bytes

(a,b,c)=>a**3+b**3+c**3==[a]+b+c

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Nothing to say.

APL (Dyalog Unicode), 16 bytes

+.*∘3=∘⍎∘∊⍕¨

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+.*∘3 sum of cubes

=∘⍎∘∊ equal to the execution of the enlisted (flattened)

⍕¨ stringification of each

Vyxal, 6 bytes

ṅ?3e∑=

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    ∑  # Sum
  3e   # of cubes
 ?     # of input
     = # Is equal to
ṅ      # Concatenation of input?