\(8x^3+4x^2y-2xy-y^3\)
\(=\left(8x^3-y^3\right)+2xy\left(2x-1\right)\)
\(=\left(2x-y\right)\left(4x^2+2xy+y^2\right)+2xy\left(2x-1\right)\)
\(=\left(2x-y\right)\left(4x^2+2xy+1+2xy\right)\)
\(=\left(2x-y\right)\left(2x+y\right)^2\)
\(8x^3+4x^2y-2xy^2-y^3\)
\(=\left(8x^3-y^3\right)+2xy\left(2x-y\right)\)
\(=\left(2x-y\right)\left(4x^2+2xy+y^2\right)+2xy\left(2x-y\right)\)
\(=\left(2x-y\right)\left(4x^2+2xy+y^2+2xy\right)\)
\(=\left(2x-y\right)\left(2x+y\right)^2\)