Question 123
Solve the system of equations for positive integer numbers $x, y, z$:
$$
\begin{cases} x^3 - 6y^2 + 27z = 132, \\ y^3 - 9z^2 + 3x = 125, \\ z^3 - 3x^2 + 12y = -68. \end{cases}
$$
$$
\begin{cases} x^3 - 6y^2 + 27z = 132, \\ y^3 - 9z^2 + 3x = 125, \\ z^3 - 3x^2 + 12y = -68. \end{cases}
$$