Question 203556
One way to do this would be to factorize 72 into its prime factors and then test each combination to see if it is a perfect cube.


However, there is a very simple method in this case.  The first four cubes (1 cubed, 2 cubed, 3 cubed, 4 cubed) are 1, 8, 27, 64.

Of these, only 1 and 8 are factors of 72.