My prof is only testing us on the strong form of induction but I can't figure out how to use it with this question.

Use induction to prove $\displaystyle n^3+2n$ is divisible by 3 for n >= 1.

Basis

$\displaystyle n_0 = 1$ then $\displaystyle (1)^3+2(1)=3$ which works

Induction Hypothesis

Let 1<=l<k and assume $\displaystyle l^3+2l$ is divisible by 3

Induction Step

$\displaystyle k^3+2k$

...and now need to use the I.H. somehow