x3+y3+z3−3xyz
=x3+y3+z3−3xyz+3xy(x+y)−3xy(x+y)
=[x3+y3+3xy(x+y)]+z3−[3xyz+3xy(x+y)]
=(x3+3x2y+3xy2+y3)+z3−3xy(z+x+y)
=(x+y)3+z3−3xy(x+y+z)
=[(x+y)3+z3]−3xy(x+y+z)
=(x+y+z)(x2+2xy+y2−xz−yz+z2)−3xy(x+y+z)
=(x+y+z)(x2+2xy+y2−xz−yz+z2−3xy)
=(x+y+z)(x2+y2+z2−xy−xz−yz)