Having a bit of trouble with this one. Can anyone help?

Many thanks.

Q.$\displaystyle n^3-n$ is divisible by 3 for $\displaystyle n \in \mathbb{N}_o$

Attempt:Step 1:For n = 1...(or P1)

1^{3}- 1 = 0, which can be divided by 3.

Step 2:For n = k...

Assume k^{3}- k can be divided by 3,

i.e. k^{3}- k = 3Z, where Z is an integer...1

Show that n = k + 1 is true...(i.e. show that P(k + 1) is true),

i.e. (k + 1)^{3}- (k + 1) can be divided by 3.

(k + 1)^{3}- (k + 1) = (k + 1)(k^{2}- k + 1) - (k + 1) = ...?