We estimate the errors of selected cubature formulae constructed by the
product of Gauss quadrature rules. The cases of multiple and (hyper-)surface
integrals over n-dimensional cube, simplex, sphere and ball are considered.
The error estimates are obtained as the absolute value of the difference
between cubature formula constructed by the product of Gauss quadrature
rules and cubature formula constructed by the product of corresponding
Gauss-Kronrod or corresponding generalized averaged Gaussian quadrature
rules. Generalized averaged Gaussian quadrature rule ?2l+1 is (2l +
1)-point quadrature formula. It has 2l + 1 nodes and the nodes of the
corresponding Gauss rule Gl with l nodes form a subset, similar to the
situation for the (2l + 1)-point Gauss-Kronrod rule H2l+1 associated with
Gl. The advantages of bG2l+1 are that it exists also when H2l+1 does not,
and that the numerical construction of ?2l+1, based on recently proposed
effective numerical procedure, is simpler than the construction of H2l+1.