We report 10-dimensional quantum dynamic calculations of the translation-rotation energy levels of two hydrogen molecules inside the cages of the structure H clathrate hydrate. For the small and medium cages, positive ground state energies are reported supporting their single occupancy, while for the large cage negative energy levels are calculated and some low-lying states are characterized for two para-H2, ortho-H2, para-D2, ortho-D2, and HD molecules inside the cage. The calculations are performed using the block improved relaxation method implemented in the multiconfiguration time-dependent Hartree (MCTDH) code.