The square root of a square root isn't a cube root:
The Cube of x = y * y * y
or x = y
3
But if:
Sqrt(Sqrt(x)) == y
Then
Sqrt(x) = y * y
And
x = (y * y) * (y * y)
or x = y
4
So as Bruno says:
private double CubeRoot(double x)
{
return Math.Pow(x, (1.0 / 3.0));
}