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Prove a^2+3ab+3b^2-1|a+b^3 implies c^3|a^2+3ab+3b^2-1

Source: 2019 Canadian Mathematical Olympiad Problem 2

March 28, 2019
number theorycube of a natural number.

Problem Statement

Let a,ba,b be positive integers such that a+b3a+b^3 is divisible by a2+3ab+3b2−1a^2+3ab+3b^2-1. Prove that a2+3ab+3b2−1a^2+3ab+3b^2-1 is divisible by the cube of an integer greater than 1.
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