  In this short note, we provide an explicit formula to compute every colored
double Tornheim's series by using double polylogarithm values at roots of
unity. When the colors are given by $\pm 1$ our formula is different from that
of Tsumura [On alternating analogues of Tornheim's double series II, Ramanujan
J. 18 (2009), 81-90] even though numerical data confirm both are correct in
almost all the cases. This agreement can also be checked rigorously by using
regularized double shuffle relations of the alternating double zeta values in
weights less than eight.
