FI-MO 2005 Problem 3

Solve the group of equations: $\begin{cases} (x + y)^3 = z (y + z)^3 = x (z + x)^3 = y \end{cases}$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.