The digits of the cube of a 3-digit number X

Question

The digits of the cube of a certain 3-digit number X are, from left to right, the square of a 2-digit number, followed by the square of another 2-digit number, followed by one digit. (Everything is base 10.) What number is X?

Answer 1

The number you're looking for is:

1,442,897

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The three digit number $x$ is:

113

The two, two digit numbers ($y$ and $z$) are:

$y = 12$ and $z = 17$; squared, these are $144$ and $289$ respectively.

The one digit number is:

7

Concatenating these together gives us:

$x^3 = 1442897$

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_{Note: I brute forced my answer since the no-computers tag wasn’t specified.}