Question 18
Find all maps $f: \mathbb{Z}_{\ge 1} \to \mathbb{Z}_{\ge 1}$ such that for any positive integers $a$ and $b$, the number
$$
af(a)^2 + bf(b)^2 + 3ab(f(a) + f(b))
$$
is a perfect cube.
$$
af(a)^2 + bf(b)^2 + 3ab(f(a) + f(b))
$$
is a perfect cube.