Probability that the number $(a^3 + b^3)$ is divisible by $3$ 
Two numbers $a$ and $b$ are chosen from the set $\{1, 2, 3, \ldots 3n\}$. Find the probability that $(a^3 + b^3)$ is divisible by $3$.

I am  not able to check whether the cube of a number is divisible by $3$.

Hint:
$a^3 + b^3 = (a+b)(a^2 - ab + b^2) = (a+b)((a+b)^2 - 3ab)$
