  In this paper we consider the existence problem of cubature formulas of
degree 4k+1 for spherically symmetric integrals for which the equality holds in
the M\"oller lower bound. We prove that for sufficiently large dimensional
minimal formulas, any two distinct points on some concentric sphere have inner
products all of which are rational numbers. By applying this result we prove
that for any d > 2 there exist no d-dimensional minimal formulas of degrees 13
and 21 for some special integral.
