$3\mid a^3+b^3+c^3$ if only if $3\mid a+b+c $ 
Prove the following equivalence: $3\mid (a^3 + b^3 + c^3) $ if and only if $3\mid (a + b + c) $.

My try:
I know $a^3 + b^3 + c^3 = (a + b + c) (a^2 + b^2 + c^2 – ab – bc – ca) + 3abc$, but I can't seem to proceed from here.
Thanks all!

Very short with Lil' Fermat:
for any $x\in\mathbf Z$, $\;x^3\equiv x\mod 3$. Hence $\;a^3+b^3+c^3\equiv a+b+c\mod 3$.
