We present a measurement of atmospheric tau neutrino appearance from oscillations with three years of data from the DeepCore subarray of the IceCube Neutrino Observatory. This analysis uses atmospheric neutrinos from the full sky with reconstructed energies between 5.6 and 56 GeV to search for a statistical excess of cascadelike neutrino events which are the signature of ντ interactions. For CC+NC (CC-only) interactions, we measure the tau neutrino normalization to be 0.73−0.24+0.30 (0.57−0.30+0.36) and exclude the absence of tau neutrino oscillations at a significance of 3.2σ (2.0σ) These results are consistent with, and of similar precision to, a confirmatory IceCube analysis also presented, as well as measurements performed by other experiments.