Show that $\displaystyle n(n^2 - 1)$ is divisible by 24 when n is an odd number.

What I've got so far is a lemma that the square of any odd number is of the form 8q + 1.

So I kinda have... $\displaystyle n(8q + 1 - 1)=8nq$

This is where I got stuck... please help lol

(good to see LaTeX up )