Recall that squares are congruent to $ 0, 1 \bmod 4$ and that cubes are congruent to $ 0, 1, -1 \bmod 9$. No sum of squares is congruent to $ 3 \bmod 4$ and no sum of cubes is congruent to $ 4 \bmod 9$, so we can take the positive integers congruent to $ 31 \bmod 36$.