Measurements are reported of the WZ and ZZ production cross sections in proton-proton collisions at sqrt{s} = 8 ,text {TeV} in final states where one Z boson decays to b-tagged jets. The other gauge boson, either W or Z, is detected through its leptonic decay (either mathrm {W}rightarrow mathrm {e}nu , mathrm {mu }nu or mathrm {Z}rightarrow mathrm {e}^+mathrm {e}^-, mathrm {mu ^+}mathrm {mu ^-}, or {nu }overline{nu }). The results are based on data corresponding to an integrated luminosity of 18.9 fb^{-1} collected with the CMS detector at the Large Hadron Collider. The measured cross sections, sigma (mathrm {p}mathrm {p}rightarrow mathrm {W}mathrm {Z}) = 30.7 pm 9.3,text {(stat.)} pm 7.1,text {(syst.)} pm 4.1,text {(th.)} pm 1.0,text {(lum.)} ,text {pb} and sigma (mathrm {p}mathrm {p}rightarrow mathrm {Z}mathrm {Z}) = 6.5 pm 1.7,text {(stat.)} pm 1.0,text {(syst.)} pm 0.9,text {(th.)} pm 0.2,text {(lum.)} ,text {pb} , are consistent with next-to-leading order quantum chromodynamics calculations.