The formation of helium clusters in a copper crystal has been studied by means of ab initio calculations. Several He atoms have been placed either inside an n vacancy previously created or as interstitials inside the initially perfect bulk matrix. Based on density functional theory techniques, our results show that the first He atom inside the perfect crystal prefers a tetrahedral position instead of an octahedral as previously reported. When n vacancies are formed in the structure, He atoms start to aggregate forming small bubbles at these sites rather than at interstitial positions. The calculated formation and binding energies confirm the deep trapping and the stability of He atoms inside vacancies, as is well known for other metals. For a given number of He atoms inside an n vacancy, N He, the minimum formation energy is found when N He is equal to the number of vacancies n. Within each n vacancy, the formation energy increases (almost) linearly with the number of He atoms until N He reaches the number of vacancies n. From this point onwards, the addition of new He atoms to the system implies a higher energy cost and consequently an abrupt decrease in the binding energy.