Measurements are reported of the WZ and ZZ production cross sections in proton-proton collisions at (\sqrt{s})=8TeV 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 (W \to e\upsilon, \mu\upsilon) or (Z \to e^+e^-), (\mu^+\mu^-), or (\upsilon\overline{\upsilon})). 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(pp \to WZ)) = 30.7 ± 9.3 (stat.) ±7.1 (syst.) ±4.1 (th.) ±1.0 (lum.) pb and (\sigma(pp \to ZZ)) = 6.5 ± 1.7 (stat.) ± 1.0 (syst.) ± 0.9 (th.) ± 0.2 (lum.) pb, are consistent with next-to-leading order quantum chromodynamics calculations.