In this contribution, we have provided and extensively documented an open-source software code for predicting two-dimensional electron gas formation in heterostructure core-shell nanowires. The algorithms in the HADO-KEN software utilize a robust finite element procedure that solves coupled Schrödinger and Poisson equations selfconsistently for a variety of geometries, doping densities, and external boundary conditions. Most importantly, the HADOKEN software can be downloaded from the Computer Physics Communications International Computer Program Library to investigate material composition effects, bandgap alignment, doping density, and cross-sectional size on Fermi gas formation in a variety of nanowire configurations. In addition, the user-friendly MATLAB code serves as a starting point for researchers that may need minor modifications of the well-documented source code to simulate other materials and geometries beyond those discussed in this work.