Factorize $2a^3 - b^3 - c^3$ I need to factorize the expression $2a^3 - b^3 - c^3$. I see that one zero is achieved when $a=b=c$, but I can't find the factor(s).

Writing
$$
2a^3-b^3-c^3=a^3-b^3+a^3-c^3=(a-b)(a^2+ab+b^2)+(a-c)(a^2+ac+c^2)
$$
We can see that we have simple factorizations if $a=b$ or $a=c$ or $b=c$ and also for $b+a=c$. But in general we cannot find a factorization for all real values of $a,b,c$.
