Results are presented from a search for production of Higgs boson pairs (HH) where one boson decays to a pair of b quarks and the other to a τ lepton pair. This work is based on proton-proton collision data collected by the CMS experiment at s=8 TeV, corresponding to an integrated luminosity of 18.3 fb-1. Resonant and nonresonant modes of HH production have been probed and no significant excess relative to the background-only hypotheses has been found in either mode. Upper limits on cross sections of the two HH production modes have been set. The results have been combined with previously published searches at s=8 TeV, in decay modes to two photons and two b quarks, as well as to four b quarks, which also show no evidence for a signal. Limits from the combination have been set on resonant HH production by an unknown particle X in the mass range mX=300 GeV to mX=1000 GeV. For resonant production of spin 0 (spin 2) particles, the observed 95% CL upper limit is 1.13 pb (1.09 pb) at mX=300 GeV and to 21 fb (18 fb) at mX=1000 GeV. For nonresonant HH production, a limit of 43 times the rate predicted by the standard model has been set.