ILL 1984 Problem 55

Let $a, b, c$ be natural numbers such that $a+b+c = 2pq(p^{30}+q^{30}), p > q$ being two given positive integers. $(a)$ Prove that $k = a^3 + b^3 + c^3$ is not a prime number. $(b)$ Prove that if $a\cdot b\cdot c$ is maximum, then $1984$ divides $k$ .