MathNet 2012 Question 86

Integers $a$, $b$, $c$ are such that $a + b + c$ is divisible by $6$, and $a^2 + b^2 + c^2$ is divisible by $36$. Does it imply that $a^3 + b^3 + c^3$ is divisible by

a) $8$;
b) $27$?