A cubature formula of the ninth degree of accuracy for a hypercube (Q1975115)

A cubature formula for calculating integrals over a hypercube in \( \mathbb{R}^n\) is obtained. The author uses the Sobolev theorem to construct this cubature formula. This formula is invariant with respect to all transformations of the hyperoctahedron into itself and is exact for all polynomials of a degree not greater than nine. The author calculates the parameters of the cubature formula for any \(n \geq 3\), where \(n\) is the dimension of space \(\mathbb{R}^n\).