$\left\{\begin{matrix} x^{3} +x^{2}+ 2x = 2y^{3}+ 1\\ y^{3} +y^{2}+ 2y = 2z^{3}+ 1\\ z^{3} +z^{2}+ 2z = 2x^{3}+ 1 \end{matrix}\right.$