Equal sums of two cubes of quadratic forms

We give a complete description of all solutions to the equation f13 + f 23 = f 33 + f 43 for quadratic forms fj [x,y] and show how Ramanujan's example can be extended to three equal sums of pairs of cubes. We also give a complete census in counting the number of ways a sextic p [x,y] can be written as a sum of two cubes. The extreme example is p(x,y) = xy(x4 - y4), which has six such representations.