The controlled growth of nanowires (NWs) with dimensions comparable to the Fermi wavelengths of the charge carriers allows fundamental investigations of quantum confinement phenomena. Here, we present studies of proximity-induced superconductivity in undoped Ge/Si core/shell NW heterostructures contacted by superconducting leads. By using a top gate electrode to modulate the carrier density in the NW, the critical supercurrent can be tuned from zero to greater than 100 nA. Furthermore, discrete sub-bands form in the NW due to confinement in the radial direction, which results in stepwise increases in the critical current as a function of gate voltage. Transport measurements on these superconductor-NW-superconductor devices reveal high-order (n=25) resonant multiple Andreev reflections, indicating that the NW channel is smooth and the charge transport is highly coherent. The ability to create and control coherent superconducting ordered states in semiconductor-superconductor hybrid nanostructures allows for new opportunities in the study of fundamental low-dimensional superconductivity.