Surface nanoscale axial photonic resonators (SNAPRs) provide an axially structured whispering-gallery-mode platform in which nanoscale effective-radius variations produce spatially localized optical resonances. Here, we demonstrate cascaded Brillouin-Kerr microcomb generation in a SNAPR fabricated from 660 micrometer diameter silica fiber. Under continuous-wave pumping, cascaded stimulated Brillouin scattering generates first- and second-order Stokes fields that seed Kerr four-wave mixing within the cavity. The resulting nonlinear spectrum contains two comb families with a common azimuthal spacing of 100.2 GHz and a relative offset of 9.6 GHz, consistent with the Brillouin shift in silica. A low-power transmission spectrogram provides a spatially resolved modal analysis of the resonator, revealing localized resonances with loaded quality factors on the order of ten million, and optical resonance pairs compatible with the measured Brillouin spacing. These results establish SNAPRs as a platform for studying cascaded stimulated Brillouin scattering, Kerr four-wave mixing, and comb formation in axially structured whispering gallery resonators.