Searches for both resonant and non-resonant Higgs boson pair production are performed in the $hh\to bb\tau\tau, \gamma\gamma WW^*$ final states using 20.3 fb$^{-1}$ of $pp$ collision data at a center-of-mass energy of 8 TeV recorded with the ATLAS detector at the Large Hadron Collider. No evidence of their production is observed and 95% confidence level upper limits on the production cross sections are set. These results are then combined with the published results of the $hh\to \gamma\gamma bb, bbbb$ analyses. An upper limit of 0.69 (0.47) pb on the non-resonant Standard Model like $hh$ production is observed (expected), corresponding to 70 (48) times of the SM $gg\to hh$ cross section. For production via narrow resonances, cross section limits of $hh$ production from a heavy Higgs boson decay are set as a function of the heavy Higgs boson mass. The observed (expected) limits range from 2.1 (1.1) pb at 260 GeV to 0.011 (0.018) pb at 1000 GeV. These results are interpreted in the context of two simplified scenarios of the Minimal Supersymmetric Standard Model.

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