This is in relation to a problem dealing with the three-dimensional analogue of Pell's Equation. I would like to factor $ x^3+Dy^3+D^2z^3-3Dxyz $ into $\frac{1}{2}(x+Dy+D^2y)$ and another factor.
I would like just a hint on how to go about doing this as I'm pretty much stumped.
EDIT: I think the factor I was looking for is $\frac{1}{2}(x+Ny+N^2z)$ where $N=D^3$.