Sphere just defines a surface, the one you are using Integrate is a volume integral so you should use Ball[{0, 0, 0}, a]
In[]:=
Volume[Sphere[{0,0,0},a]]
Out[]=
Undefined
In[]:=
Volume[Ball[{0,0,0},a]]
Out[]=
4π
3
a
3
In[]:=
Integrate[.{x,y,z},{x,y,z}∈Ball[{0,0,0},a]]
∇
{x,y,z}
Out[]=
4π
3
a