CERN-LHC. The four-lepton ($4\ell$, $\ell = e, \mu$) production cross section is measured in the mass range from 80 to 1000 GeV using 20.3 fb$^{-1}$ of data in $pp$ collisions at $\sqrt{s}=8$ TeV collected with the ATLAS detector at the LHC. The $4\ell$ events are produced in the decays of resonant $Z$ and Higgs bosons and the non-resonant $ZZ$ continuum originating from $q\bar q$, $gg$, and $qg$ initial states. A total of 476 signal candidate events are observed with a background expectation of $26.2 \pm 3.6$ events, enabling the measurement of the integrated cross section and the differential cross section as a function of the invariant mass and transverse momentum of the four-lepton system. In the mass range above 180 GeV, assuming the theoretical constraint on the $q\bar q$ production cross section calculated with perturbative NNLO QCD and NLO electroweak corrections, the signal strength of the gluon-fusion component relative to its leading-order prediction is determined. The experimental fiducial region for four-lepton analysis is defined as: - 4e, 4mu or 2e2mu. - The leading dilepton pair is selected as the one with invariant mass closest to the Z-boson mass. - The sub-leading dilepton pair is selected among the remaining possible pairs with largest invariant mass. - ptLepton > 6 (7) GeV for muons (electrons). - |etaLepton| < 2.7 (2.5) for muons (electrons). - ptDilepton > 2 GeV. - ptLepton > 20, 15, 8 (10) GeV for leading, sub-leading and third muons (electrons). - min(DeltaR(l,l)) > 0.1 (0.2) for same- (different-) flavour leptons. - Leading dilepton invariant mass between 50 and 120 GeV. - Sub-leading dilepton invariant mass between 12 and 120 GeV. - All same-flavor opposite-sign lepton pairs should have invariant mass larger than 5 GeV. - Four-lepton invariant mass between 80 and 1000 GeV. UPDATE 25/04/2016: Covariance matrices were previously given without systematic uncertaintis. This mistake has been corrected.