Measurements are reported of the WZ and ZZ production cross sections in proton-proton collisions at sqrt(s) = 8 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 W to e nu, mu nu or Z to e+ e-, mu+ mu-, or nu anti-nu). The results are based on data corresponding to an integrated luminosity of 18.9 inverse femtobarns 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.