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 $\displaystyle a(a^2-1) = (2w+1)[(8k+1)^2-1] = 128k^2w+32kw+64k^2+16k $

But now, how do I factor out 24?