A complete set of migration energies for a He atom moving inside the bulk of the bcc-W and fcc-Cu crystals has been calculated in different configurations using the nudged elastic band method as a tool within the density functional theory formalism. Although the most stable site in the perfect crystal is the tetrahedral position in both cases, the He atoms jump preferentially between two first nearest tetrahedral positions in tungsten, while they migrate through an octahedral position in the case of Cu. As reported before, the He atoms are trapped when they find an n-vacancy. Our results show that the migration energies are lower when the n-vacancies do not contain He atoms, suggesting that vacancies are stabilized and their mobility is reduced by helium trapping, that may end up in bubble coalescence, in agreement with previous findings. The migration energy of the clean n-vacancy decreases as the number n increases, at least up to n = 3, while the situation when He atoms are inside the vacancies is a little bit more complicated. In all the analyzed cases, the energy barriers in W are higher than in Cu. Additionally, a complete analysis of the evolution of the electronic density of states has been performed, that leads to the confirmation of a non-negligible He-metal interaction that significantly contributes to the trapping of helium atoms inside the n-vacancies.