UZ-MO 2014 Problem 2

Find all functions $f:R\rightarrow R$ such that $f(x^3)+f(y^3)=(x+y)(f(x^2)+f(y^2)-f(xy))$ for all $x,y\in R$ .

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.