The evaluation of lattice sums as well as stress lattice sums encountered in the periodic fast multipole method is reinvestigated. Simple, accurate, and efficient recurrence expressions for such sums following the ideas of the renormalization method are derived. The first few nonzero lattice sum terms in a three-dimensional cubic lattice are computed and given in Tables. The practical considerations accompanying the computation of the sums such as convergence and accuracy are discussed. (C) 2004 American Institute of Physics.