To start you off this works:
InterpolatingPolynomial[{{{4, 4}, 52}, {{4, 6}, 120}, {{4, 8},
212}, {{6, 4}, 120}, {{6, 6}, 256}, {{6, 8}, 432}, {{8, 4},
212}, {{8, 6}, 432}, {{8, 8}, 708}, {{10, 6}, 648}, {{10, 8},
1040}}, {w, z}]//Expand
(4 - w^2 - 3 w z + w^2 z - z^2 + w z^2)
Maybe you did not have enough points before to uniquely determine all the coefficients.