The scalar-indexed Warren-Cowley order parameters for the perfectly orderedCu3Auand CuZn alloys are calculated with the aid of Waring's theorem from number theory. Cowley and Klein have incorrectly reported these parameters forCu3Auas being one for even-order shells (of neighbors) and−13for odd-order shells. We show that these parameters are equal to one for those shells with radiusd(2k)12,k ≠ 4a(8b + 7), and−13for those shells with radiusd(2k + 1)12, wherea,b,kare nonnegative integers anddis the radius of the first shell in the fcc lattice. For the ordered form of CuZn (beta brass), we find that the order parameters are one for those shells with radiusd(k)12,k ≠ 4a(8b + 7), and minus one for those shells with radius(d/2)(8k − 5)12, wherea,bare nonnegative integers,kis a positive integer, anddis the nearest distance between two like atoms. Five theorems proved in this paper are the basis for the preceding results and are also useful in the study of point defects in cubic crystals and in the study of ionic crystals. Formulas are given for the radii of the shells of lattice points about given points, both lattice and interstitial points, in cubic lattices.