What is the least four-digit whole number that is both a perfect square and a perfect cube?
Let $n$ be the least four-digit whole number that is both a perfect square and a perfect cube.  In order for a number to be a perfect cube and a perfect square, it must be a perfect sixth power. Now we choose the smallest $a$ such that $n$ is four-digit: $2^6=64$, $3^6=729$, $4^6=4096$. Thus, $n=\boxed{4096}$.