x^3-8y^3-z^3-6xyz
=(x-2y-z)(x^2+4y^2+z^2)+2x^2y+x^2z-4y^2x+4y^2z-z^2x-2z^2y-6xyz
=(x-2y-z)(x^2+4y^2+z^2)+2x^2y+y^2z-2xyz +x^2z-4y^2x-2xyz -z^2x-2z^2y-2xyz
=(x-2y-z)(x^2+4y^2+z^2)-(x-2y-z)(-2xy+2yz-xz)
=(x-2y-z)(x^2+4y^2+z^2+2xy-2yz+xz)