Question 162
Find possible positive solutions $(x, y, z)$ for the given system of equations:
$$
\begin{cases}
x + y^2 = 2z^3, \\
y + z^2 = 2x^3, \\
z + x^2 = 2y^3.
\end{cases}
$$
$$
\begin{cases}
x + y^2 = 2z^3, \\
y + z^2 = 2x^3, \\
z + x^2 = 2y^3.
\end{cases}
$$