assume we have the regression model: $$Y = b_0 + b_1 x_1 + \dots + b_k x_k + \varepsilon $$

I know the formulas for all type III sum of squares for the regression terms except the formula for SS of the intercept term.

The type III SS of the regression term $x_i$ $(i=1,\dots, k)$ is equal to:
$$SS(x_i|x_1,\dots,x_{i-1},x_{i+1},\dots,x_k) = SS(x_1,\dots,
x_k) -SS(x_1,\dots,x_{i-1},x_{i+1},\dots,x_k) $$
where $SS(x_{i_1},\cdots,x_{i_m})$, $({i_1},\cdots,{i_m} \in \{1,\dots,k\})$, is defined as the $SSR$ of the regression model:
$$Y=\beta_{i_0}+\beta_{i_1}x_{i_1}+\cdots+\beta_{i_1}x_{i_m} + \epsilon$$

I just need to know what is the mathematical formula for type III SS of the **intercept term** or where can i find this formula? I cannot find any reference has this formula and I have tired of searching for it!

In R the type III SS for the intercept term and the other terms can be calculated by the function car::Anova().