division by lambda: x^3 +y^3 = z^3 where x,y,z are quadratic

[chrisl]

Let x^3 + y^3 = z^3 where x, y, and z are quadratic integers in Q(sqrt -3)

Prove that lambda must divide one of x, y, and z, where lambda = (3 + sqrt[-3])/2.

I need to reduce the equation mod (lambda^3) but I don't know how to. Could I have help?