The number of pairs of positive integers \(x\) , \(y\) which solve the equation \[x^3 + 6x^2y + 12xy^2 + 8y^3 = 2^{30}\] is

\(0\),

\(2^6\),

\(2^9-1\),

\(2^{10}+2\).

The number of pairs of positive integers \(x\) , \(y\) which solve the equation \[x^3 + 6x^2y + 12xy^2 + 8y^3 = 2^{30}\] is

\(0\),

\(2^6\),

\(2^9-1\),

\(2^{10}+2\).