This paper presents a measurement of the double-differential cross section for the Drell-Yan Z/\u3b3 17 \u2192 \u2113+\u2113 12 and photon-induced \u3b3\u3b3 \u2192 \u2113+\u2113 12 processes where \u2113 is an electron or muon. The measurement is performed for invariant masses of the lepton pairs, m\u2113\u2113, between 116 GeV and 1500 GeV using a sample of 20.3 fb 121 of pp collisions data at centre-of-mass energy of s=8 TeV collected by the ATLAS detector at the LHC in 2012. The data are presented double differentially in invariant mass and absolute dilepton rapidity as well as in invariant mass and absolute pseudorapidity separation of the lepton pair. The single-differential cross section as a function of m\u2113\u2113 is also reporte...