Prove that if a is an odd integer, then 24 | a(a^2-1).

Proof. from a previous in my homework, I know that the square of an odd integer can be written in the form of 8k + 1.

Now, let a = 2w + 1 and a^2 = 8k + 1, for some integers w and k.

Then

But now, how do I factor out 24?