If $$V$$ is the gravitational potential due to sphere of uniform density on its surface, then its value at the centre of sphere will be:

For a uniform solid sphere of mass M and radius R:

Gravitational potential at the surface:

$$V_{surface} = -\frac{GM}{R}$$

Gravitational potential at the centre:

$$V_{centre} = -\frac{3GM}{2R}$$

Since $$V = V_{surface} = -\frac{GM}{R}$$:

$$V_{centre} = -\frac{3GM}{2R} = \frac{3}{2}\left(-\frac{GM}{R}\right) = \frac{3}{2}V$$

The gravitational potential at the centre is $$\frac{3V}{2}$$.

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