A perfect square is a number that has an exact square root, for example, 4, 9, 16 are perfect square.
A perfect cube is a nunmber that has an exact cubic root, for example, 8, 27 are perfect cubes.
Having said that, 32 is not a perfect square nor a perfect cube, since we can take a square or cubic root and have an extact number as a resuslt.
However, 81 is a perfect square, but it's not a perfect cube, since it's square root is 9, but it's cubic root is a decimal number 8 (not exact).