(x-y)^3+(y-z)^3=((x-y)+(y-z))((x-y)^2-(x-y)(y-z)+(y-z)^2)
=-(z-x)(x^2-2xy+3y^2-xy+xz-yz-2yz+z^2)

(x-y)^3+(y-z)^3+(z-x)^3
=-(z-x)(x^2-2xy+3y^2-xy+xz-yz-2yz+z^2-(z^2-2zx+x^2))
=-(z-x)(-3xy+3y^2+3xz-3yz)
=-3(z-x)(y^2-(x+z)y+xz)
=-3(z-x)(y-x)(y-z)
=3(x-y)(y-z)(z-x)