Prove that the determinant is $(a-b)(b-c)(c-a)(a+b+c)$ I have the determinant : 
\begin{vmatrix}
1 &1 &1 \\
a &b &c \\
a^3 &b^3 &c^3 \\
\end{vmatrix}
How do I prove that this determinant is equal to
$$ (a-b)(b-c)(c-a)(a+b+c) $$

Hint: $a^3 -b^3$ $=$ $(a-b)(a^2 + +ab + b^2)$
Subtract column $1$ from column $2$ and then column $2$ from column $3$.
