\(a^3-b^3+c^3+3abc\)
\(=\left(a-b\right)^3+c^3+3abc+3a^2b-3ab^2\)
\(=\left[\left(a-b\right)^3+c^3\right]+3ab\left(c+a-b\right)\)
\(=\left(c+a-b\right)\left[\left(a-b\right)^2-\left(a-b\right)c+c^2\right]+3ab\left(c+a-b\right)\)
\(=\left(c+a-b\right)\left(a^2-2ab+b^2-ac+bc+c^2+3ab\right)\)
\(=\left(c+a-b\right)\left(a^2+b^2+c^2+ab-ac+bc\right)\)