We continue the construction of a cubature formulas for approximate calculations of multiple integrals, which is starting in [8], for regions: the Sphere, the Cone, the Cylinder, the Torus, by using combinations, or products, of the generalized Turán quadratures (see [4],[5],[7]). Here $s\in N\cup {0}$. The particular case $s=0$ is given in [l],[12]. Some numerical examples are included.