Suggestion

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

  1. \(0\),

  2. \(2^6\),

  3. \(2^9-1\),

  4. \(2^{10}+2\).

Can we factorise the left hand side of the equation?