SMO 2008 Open Round 1 Question 19

Let $a,b,c,d,e$ be five numbers satisfying $a+b+c+d+e=0$ and $abc+abd+abe+acd+ace+ade+bcd+bce+bde+cde=2008$. Find $a^3+b^3+c^3+d^3+e^3$.