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