Differential and integrated fiducial cross sections for the production of four leptons via the $\mathrm{H} \rightarrow 4\ell$ decays ($\ell = \mathrm{e}$, $\mu$) are measured in pp collisions at $\sqrt{s} =$ 7 and 8 TeV. Measurements are performed with data corresponding to integrated luminosities of 5.1 fb$^{-1}$ at 7 TeV, and 19.7 fb$^{-1}$ at 8 TeV, collected with the CMS experiment at the LHC. Differential cross sections are determined as functions of the transverse momentum and rapidity of the four-lepton system, accompanying jet multiplicity, transverse momentum of the leading jet, and difference in rapidity between the Higgs boson candidate and the leading jet. A measurement of the $\mathrm{Z} \rightarrow 4\ell$ cross section, and its ratio to the $\mathrm{H} \rightarrow 4\ell$ cross section is also performed. All cross sections are measured within a fiducial phase space defined by the requirements on lepton kinematics and event topology. The integrated $\mathrm{H} \rightarrow 4\ell$ fiducial cross section is measured to be $0.56^{\rm +0.67}_{\rm -0.44} \mathrm{(stat)} ^{\rm +0.21}_{\rm -0.06} \mathrm{(syst)}$ fb at 7 TeV, and $1.11^{\rm +0.41}_{\rm -0.35} \mathrm{(stat)} ^{\rm +0.14}_{\rm -0.10} \mathrm{(syst)}$ fb at 8 TeV. The measurements are found to be compatible with theoretical calculations based on the standard model.

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