There is a formula which relate the roots: $$(\sum \alpha)^2=\sum \alpha^2-2\sum \alpha\beta$$
However I have kind of forgotten the formula which relates the $\sum \alpha^3$. (I think it's only used for cubic equations)
The formula kind of look like this $$(\sum \alpha)^3=\sum \alpha^3+3\sum \alpha\sum\alpha\beta+3\sum \alpha\beta\gamma$$ (This I think is wrong because I used it and got a wrong answer)
Can somebody please provide the formula?(I tried searching on Google but couldn't find it)
P.S. $\alpha,\beta,\gamma$ are roots of a general polynomial equation.