This paper presents some theoretical results on the sphere coverage problem in the n-dimensional space. These results refer to the minimal number of spheres, denoted by $N_k\left(a\right)$, to cover a cuboid. The first properties outline some theoretical results for the numbers $N_k\left(a\right)$, including sub-additivity and monotony on each variable. We use then these results to establish some lower and upper bounds for $N_k\left(a\right)$, as well as for the minimal density of spheres to achieve k-coverage. Finally, a computation is proposed to approximate the $N_k\left(a\right)$ numbers, and some tables are produced to show them for 2D and 3D cuboids.