If a + b + c = 0, then the value of a3 + b3 + c3 is?

Answer: Option C

$$\begin{array}{rl}& a+b+c=0\\ & \text{Let, }{a}^3+b^3+c^3=T\end{array}$$
$$\Rightarrow a^3+b^3+c^3-3abc=\frac{1}{2}\left(a+b+c\right)$$      $$\left[{\left(a-b\right)}^2+{\left(b-c\right)}^2+{\left(c-a\right)}^2\right]$$
$$\Rightarrow a^3+b^3+c^3-3abc=\left(0\right)$$     $$\left[{\left(a-b\right)}^2+{\left(b-c\right)}^2+{\left(c-a\right)}^2\right]$$
$$\begin{array}{rl}& \Rightarrow a^3+b^3+c^3-3abc=0\\ & \Rightarrow a^3+b^3+c^3=3abc\end{array}$$