Estimate of the remainder of a cubature formula for a hypersphere

An estimate is given for the remainder term of a cubature formula of special type for calculating an integral over an $n$-dimensional sphere. The algebraic degree of precision of the formula is the highest among formulas of this type and is equal to $4p-1$. Appearing in the estimate is an upper bound of the absolute values of all the partial derivatives of the integrand function of order $4p$ in the domain of integration.