I'm probably just being dumb now, but I cannot seem to prove that $\displaystyle n^3+14n$ is divisible by 3. I am trying induction:

Base case: $\displaystyle n=1$. Then 1+15=15, which is divisible by 3.

Inductive step:

$\displaystyle (n+1)^3+14(n+1)$

$\displaystyle = n^3+3n^2+17n+15$

$\displaystyle = (n+1)^2(n^2+2n+15)$

But then from here, I'm stuck. Any suggestions?

EDIT: this is for all ints >= 0.

Thanks in advance!