x^3-3x^2y+3xy^2-y^3
=(x^3-y^3)-(3x^2y-3xy^2)
=(x-y)(x^2+xy+y^2)-3xy(x-y)
=(x-y)(x^2+xy+y^2-3xy)
=(x-y)(x^2-2xy+y^2)
=(x-y)(x-y)^2
=(x-y)^3