Find all $f:\mathbb{R}\rightarrow\mathbb{R}$ which satisfy

$$f(x^3)+f(y^3)=(x+y)(f(x^2)+f(y^2)-f(xy))$$ for all $x,y\in\mathbb{R}$.

This is a contest math problem, and I have very little experience with functional equations. Thus I sadly have no progress to show. Admittedly, I'm posting this just to get some input on good strategies and solutions.


merged by Jyrki Lahtonen Jun 22 '15 at 11:22

This question was merged with Strategies to find the set of functions $f:\mathbb{R}\to\mathbb{R}$ which satisfy a given functional equation because it is an exact duplicate of that question.