The length of diagonal of the cube of each side b is $\sqrt{3b^2}$ = $b\sqrt{3}$ Distance of any of the vertices from the centre of cube, = $\sqrt{\frac{3}{2}}$ b V = 8 × $\frac{1}{4\pi\varepsilon_0}\frac{q}{r}$ = 8 × $\frac{1}{4\pi\varepsilon_0}\frac{q}{\frac{\sqrt{3}b}{2}}$ or V = $\frac{4q}{\sqrt{3}\pi\varepsilon_0 b}$ E = 0, as electric field at centre due to a charge at any corner of cube is just equal and opposite to that of another charge at diagonally opposite corner of cube.