Consider an arbitrary shaped uncharged conductor where potential is V₀ with two cavities as shown. There is no net charge on the conductor. Charges q₁ and q₂ are placed inside the cavities at their centers

Field at $p_1$ is only due to  $q_1$.

$E_{p_1}=\frac{q_1}{4\pi {\epsilon }_0{r}_1^2}$

$V_{p_1}=\frac{k{q}_1}{4\pi {\epsilon }_0{r}_1}-\frac{k{q}_1}{4\pi {\epsilon }_0{r}_{01}}+V_0$

$=\frac{k{q}_1}{4\pi {\epsilon }_0}\left(\frac{1}{r_1}-\frac{1}{r_{01}}\right)+V_0$

Self-energy of the conductor= $\frac{1}{2}\int Vdq$

Since charge on conductor is zero. Potential is zero and hence potential energy is zero.