Producing dense packings of cubes

In this paper we consider the problem of packing a set of d-dimensional congruent cubes into a sphere of smallest radius. We describe and investigate an approach based on a function ψ called the maximal inflation function. In the three-dimensional case, we localize the contact between two inflated cubes and we thus improve the efficiency of calculating ψ. This approach and a stochastic algorithm are used to find dense packings of cubes in 3 dimensions up to n=20. For example, we obtain a packing of eight cubes that improves on the cubic lattice packing.