Cubature formulas for integrals over the hyperoctahedron \(O_{n}\) in \({\mathbb{R}}^{n}\) are derived. These formulas are invariant under the group of all orthogonal transformations of \(O_{n}\). The result is based on a theorem by S. L. Sobolev (1962). Two of these formulas are exact for polynomials of degree not greater than seven, and one more is exact for polynomials of the degree not greater than five. The parameters of the formulas are calculated by using of a computer program realized in FORTRAN. The number of nodes is compared with the known estimates given in the book by I. P. Mysovskikh.