If the radius of a sphere is equal to the length of the sides of a cube, are their volumes equal? why or why not?

Well I don't know !
Let's get together and look into it.

The radius of the sphere and the side of the cube have
the same length.  Let's call that length ' L ' .

The volume of the cube is    ( L³ ) .

The volume of the sphere is      (4/3) (pi) (L³) .

Taking several minutes to examine those quantities carefully,
I noticed that

       ( L³ )   is not equal to   (4/3) (pi) (L³) .

So it's pretty clear that the cube and the sphere
DO NOT have equal volumes.