  The sum formula is a basic identity of multiple zeta values that expresses a
Riemann zeta value as a homogeneous sum of multiple zeta values of a given
dimension. This formula was already known to Euler in the dimension two case,
conjectured in the early 1990s for higher dimensions and then proved by
Granville and Zagier independently. Recently a weighted form of Euler's formula
was obtained by Ohno and Zudilin. We generalize it to a weighted sum formula
for multiple zeta values of all dimensions.
