\(x^3+3x^2y+3xy^2+y^3-8x^3\)
\(=\left(x+y\right)^3-8x^3\)
\(=\left(x+y\right)^3-\left(2x\right)^3\)
\(=\left[\left(x+y\right)-\left(2x\right)\right]\left[\left(x+y\right)^2+\left(x+y\right)\left(2x\right)+\left(2x\right)^2\right]\)
\(=\left(x+y-2x\right)\left[x^2+2xy+y^2+2x^2+2xy+4x^2\right]\)
\(=\left(x+y-2x\right)\left(7x^2+4xy+y^2\right)\)