The author uses the method of reproducing kernels [cf. I. P. Mysovskih, Sov. Math., Dokl. 9, 277–280 (1968); translation from Dokl. Akad. Nauk SSSR 178, 1252–1254 (1968; Zbl 0176.14404)] for constructing cubature formulae for an invariant integral. Generalizations of H. M. Möller’s results [Polynomideale und Kubaturformeln. Diss. Univ. Dortmund (1973)] are given.