n-boson energies at finite volume and three-boson interactions

We calculate the volume dependence of the ground-state energy of n identical bosons with short-range repulsive (or weakly attractive) interactions in a periodic spatial volume of side L, up to and including terms of order L(-6). With this result, Lattice-QCD calculations of the ground-state energies of three or more pions will allow for a systematic extraction of the three-pion interaction at this order in the volume expansion.