Show that $n(n^2-1)$ is divisible by 24, if $n$ is an odd integer greater than $2$. How can I show that $n(n^2-1)$ is divisible by 24, if $n$ is an odd integer greater than $2$?
I am thinking that since odd numbers have the form of $2n-1$ in which if it is to be more than $2$, it will be $2n-1+1 = 2n+1$. So would it be correct to use this and try solving through induction?

Easier with congruences:


*

*$n^3-n\equiv 0\mod 3$ for all $n$ (that's Little Fermat's theorem), 

*If $n$ is odd, $n\equiv \pm 1,\pm3\mod 8$, so $\;n^2\equiv 1\mod8$,

*last, use the Chinese remainder theorem.

