This paper will devote to construct a family of fifth degree cubature
formulae for n-cube with symmetric measure and n-dimensional spherically
symmetrical region. The formula for n-cube contains at most n2+5n+3 points
and for n-dimensional spherically symmetrical region contains only n2+3n+3
points. Moreover, the numbers can be reduced to n2+3n+1 and n2+n+1 if
n=7 respectively, the later of which is minimal.Comment: 13 page