I had to prove by induction that n³ - n is divisible by 3.

What I did was expanded (n + 1)³ - (n + 1) and simplified it and I got n(n + 1)(n + 2). From my assumption that it is true for all n, I can see that this is also divisible by n and so it has been proved for the (n + 1) term.

Is that correct?