If $a + b + c = 0$, what is the value of $a^3 + b^3 + c^3$?

The identity $a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2-ab-bc-ca)$ has right-hand side zero when $a+b+c=0$. Therefore $a^3+b^3+c^3=3abc$, so option A is correct. The sum being zero does not by itself imply that the sum of cubes is zero.