The electronic properties of thin, nanometer scale GaAs quantum well tubes embedded inside the AlGaAs shell of a GaAs core-multishell nanowire are investigated using optical spectroscopies. Using numerical simulations to model cylindrically and hexagonally symmetric systems, we correlate these electronic properties with structural characterization by aberration-corrected scanning transmission electron microscopy of nanowire cross sections. These tubular quantum wells exhibit extremely high quantum efficiency and intense emission for extremely low submicrowatt excitation powers in both photoluminescence and photoluminescence excitation measurements. Numerical calculations of the confined eigenstates suggest that the electrons and holes in their ground states are confined to extremely localized one-dimensional filaments at the corners of the hexagonal structure which extend along the length of the nanowire.