What is a palindromic cube?

A palindromic cube is a number that is both a cube of an integer and a palindrome, meaning it reads the same forwards and backwards. For example, ( 1^3 = 1 ) and ( 2^3 = 8 ) are not palindromic, but ( 3^3 = 27 ) is also not palindromic. However, ( 4^3 = 64 ) is likewise not palindromic. An example of a palindromic cube is ( 5^3 = 125 ), as it reads the same in reverse form, although it is important to note that actual palindromic cubes in their entirety are rare.