MathNet 2019-part-02 — 184 problems (EN–VI) Question 77

Let $a$ and $b$ be positive integers such that $a + b^{3}$ is divisible by $a^{2} + 3 a b + 3 b^{2} - 1$. Prove that $a^{2} + 3 a b + 3 b^{2} - 1$ is divisible by the cube of an integer greater than 1.