Question 148
Find all functions $f : \mathbb{Z} \to \mathbb{Z}$ such that
$$
f(a^3) + f(b^3) + f(c^3) + 3f(a+b)f(b+c)f(c+a) = (f(a+b+c))^3
$$
for all $a, b, c \in \mathbb{Z}$.
$$
f(a^3) + f(b^3) + f(c^3) + 3f(a+b)f(b+c)f(c+a) = (f(a+b+c))^3
$$
for all $a, b, c \in \mathbb{Z}$.