(x+y+z)^3-x^3-y^3-z^3=3(x^2y+xy^2+y^2z+yz^2+z^2x+zx^2)+6xyz
=3{(y+z)x^2+(y^2+z^2+2yz)x+yz(y+z)}
=3(y+z){x^2+(y+z)x+yz}
=3(y+z)(x+y)(x+z)
=3(x+y)(y+z)(z+x)