Let $M$ be the mass of the sphere of radius $R$.

Gravitational potential at any point $P$ due to the solid sphere can be written as,

$\left(1\right)$ At all points lies inside $\left(r<R\right)$ the sphere is,

$V_P=-\frac{GM}{2R^3}(3R^2-r^2)$

$\left(2\right)$ On the sphere $\left(r=R\right)$ is, $V_P=-\frac{GM}{R}$

$\left(3\right)$ At any point outside the sphere $\left(r>R\right)$ is,

$V_P=-\frac{GM}{r}$