4. Find the integer solutions $(x, y, z)$ of the system of equations
$$
\left\{\begin{array}{l}
x+y+z=0, \\
x^{3}+y^{3}+z^{3}=-18
\end{array}\right.
$$
(Tip: Note that $x y z \neq 0$. Using Newton's formula, we derive $x y z = -6$. Thus, the system of equations has 6 sets of integer solutions: $(x, y, z) = (1,2,-3), (2,1,-3), (1,-3,2), (2,-3,1), (-3,1,2), (-3,2,1)$.