  We prove sum formulas for double polylogarithms of Hurwitz type, that is,
involving a shifting parameter $b$ in the denominator. These formulas
especially imply well-known sum formulas for double zeta values, and sum
formulas for double $L$-values. Further, differentiating in $b$, we obtain a
kind of weighted sum formula for double polylogarithms and double $L$-values.
We also give sum formulas for partial double zeta values with some congruence
conditions. Our proofs of those sum formulas are based on certain functional
relations for double polylogarithms of Hurwitz type.
