Factorisation of algebric expression

Question

If $a+b+c+d+e=0$ than factorise $a^3+b^3 +c^3+ d^3 +e^3$. . I know that if $a+b+c+d=0$ than $a^3+b^3 +c^3+ d^3 = 3(a+b)(a+c)(a+d)$. Similarly can we say something about $a^3+b^3 +c^3+ d^3 +e^3$. It will be a great help if someone can solve it or give some hint about it.

Answer 1

We then have $$ a^3+b^3+c^3+d^3+e^3= - 3((b + c + d)^2a + (b + c)(b + d)(c + d) + (c + d + b)a^2). $$