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