Group III-V coaxial core-shell semiconducting nanowire heterostructures possess unique advantages over their planar counterparts in logic, photovoltaic, and light-emitting devices. Dimensional confinement of electronic carriers and interface complexity in nanowires are known to produce local electronic potential landscapes along the radial direction that deviate from those along the normal to planar heterojunction interfaces. However, understanding of selected electronic and optoelectronic carrier transport properties and device characteristics remains lacking without a direct measurement of band alignment in individual nanowires. Here, we report on, in the GaAs/AlxGa1-xAs and GaAs/AlAs core-shell nanowire systems, how photocurrent and photoluminescence spectroscopies can be used together to construct a band diagram of an individual heterostructure nanowire with high spectral resolution, enabling quantification of conduction band offsets.