Question 61
Find all functions $f : \mathbb{R} \to \mathbb{R}$ such that for any three real numbers $a, b, c$ that satisfy $a + f(b) + f(f(c)) = 0$, the following equality holds:
$$
f(a)^3 + b f(b)^2 + c^2 f(c) = 3abc.
$$
$$
f(a)^3 + b f(b)^2 + c^2 f(c) = 3abc.
$$