Two uniformly charged conducting spheres of radii R₁ and R₂ having charges Q₁ and Q₂ respectively are seperated by distance r. Find total electrostatic energy of this system?

Here $\mathrm{U}={\mathrm{U}}_{\text{self }}+{\mathrm{U}}_{\text{interaction }}$
${\mathrm{U}}_{\text{self }}=\frac{{\mathrm{Q}}_1^2}{8{\mathrm{\pi \epsilon }}_0{\mathrm{R}}_1}+\frac{{\mathrm{Q}}_2^2}{8{\mathrm{\pi \epsilon }}_0{\mathrm{R}}_2};{\mathrm{U}}_{\text{interaction }}=\frac{1}{4{\mathrm{\pi \epsilon }}_0}\frac{{\mathrm{Q}}_1{\mathrm{Q}}_2}{\mathrm{r}}\Rightarrow \mathrm{U}=\frac{1}{8{\mathrm{\pi \epsilon }}_0}\left\{\frac{{\mathrm{Q}}_1^2}{{\mathrm{R}}_1}+\frac{{\mathrm{Q}}_2^2}{{\mathrm{R}}_2}+\frac{2{\mathrm{Q}}_1{\mathrm{Q}}_2}{\mathrm{r}}\right\}$If the two spheres are non conducting, in this case, ${\mathrm{U}}_{\text{self }}=\frac{3{\mathrm{Q}}_1^2}{20{\mathrm{\pi \epsilon }}_0{\mathrm{R}}_1}+\frac{3{\mathrm{Q}}_2^2}{20{\mathrm{\pi \epsilon }}_0{\mathrm{R}}_2}$
So, $\mathrm{U}=\frac{1}{4{\mathrm{\pi \epsilon }}_0}\left\{\frac{3{\mathrm{Q}}_1^2}{5{\mathrm{R}}_1}+\frac{3{\mathrm{Q}}_2^2}{5{\mathrm{R}}_2}+\frac{{\mathrm{Q}}_1{\mathrm{Q}}_2}{\mathrm{r}}\right\}$