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?
The number you're looking for is:
The three digit number $x$ is:
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:
Concatenating these together gives us:
$x^3 = 1442897$
Note: I brute forced my answer since the no-computers tag wasn’t specified.