Consider a solid cube of uniform volume charge density. If V is electrostatic potential at one of the corners of cube then the potential at the centre of cube is

Let  ρ is the charge density and l is the edge length of cube. We know that potential at any point has to be proportional to charge and inversely proportional to side length of cube soV∝Ql=ρl3l=ρl2 Now, to find potential at centre, the cube of edge length l  can be considered as 8 cubes of length l/2 so the potential at centre of original can be obtained as sum of potentials due to 8 cubes (of length l/2 ) at the cornersVcentre∝8×ρl22=8ρl24=2ρl2 ∴VcentreV=2ρl2ρl2=2 ⇒Vcentre=2V