The production cross sections of the inclusive Drell-Yan processes W±→ℓν and Z/γ∗→ℓℓ (ℓ=e, μ) are measured in proton-proton collisions at s√=7  TeV with the ATLAS detector. The cross sections are reported integrated over a fiducial kinematic range, extrapolated to the full range, and also evaluated differentially as a function of the W decay lepton pseudorapidity and the Z boson rapidity, respectively. Based on an integrated luminosity of about 35  pb−1 collected in 2010, the precision of these measurements reaches a few percent. The integrated and the differential W± and Z/γ∗ cross sections in the e and μ channels are combined, and compared with perturbative QCD calculations, based on a number of different parton distribution sets available at next-to-next-to-leading order.