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In the present paper, we prove an identity for the generating function of thequadruple zeta values. Taking homogeneous parts on both sides of the identityand substituting appropriate values for the variables, we obtain the sumformula for quadruple zeta values. We also obtain its weighted analogues, whichinclude the formulas for this case proved by Guo and Xie (2009, J. NumberTheory 129, 2747--2765) and by Ong, Eie, and Liaw (2013, Int. J. Number Theory9, 1185--1198).

Use of the generating function to generalize the sum formula for quadruple zeta values