=\(a^3+3a^2.b+3a.b^2+b^3+a^3-3a^2.b+3a.b^2-b^3-2a^3-6a.b^2=0\)
\(\left(a+b\right)^3+\left(a-b\right)^3-2a\left(a^2+3b^2\right)\)
\(=a^3+3a^2b+3ab^2+b^3+a^3-3a^2b+3ab^2-b^3-2a\left(a^2+3b^2\right)\)
\(=2a^3+6ab^2-2a\left(a^2+3b^2\right)\)
\(=2a^3+6ab^2-2a^3-6ab^2\)
\(=2a^3-2a^3\)
\(=0\)