Only the error mean square is unbiased for $\sigma^2$ in general

In a multiple linear regression model $Y_i=B_0+B_1X_{i1}+\dots+B_pX_{ip}+\varepsilon_i$ with $E(\varepsilon_i)=0$, $\operatorname{Var}(\varepsilon_i)=\sigma^2$, $i=1,\dots,n$: