Problem #WSP-000121

Problem

How many cuboids are contained in an $n\times n\times n$ cube? For example, we’ve got $n^3$ cuboids of size $1\times 1\times 1$, and obviously just $1$ of size $n\times n\times n$ (which is the whole cube itself). But we also have to count how many there of size $1\times 1\times 2$, $1\times 2\times 3$, and several more.