We investigate single CoFeB nanotubes with hexagonal cross section using dynamic cantilever magnetometry (DCM). We develop both an analytical model based on the Stoner-Wohlfarth approximation and a broadly applicable numerical framework for analyzing DCM measurements of magnetic nanostructures. Magnetometry data taken at 4.2 K show the presence of a uniformly magnetized configuration at high external fields with mu M-0(s) = 1.3 +/- 0.1 T and nonuniform configurations at low fields. In this low-field regime, comparison between numerical simulations and DCM measurements supports the existence of flux-closure configurations. Crucially, evidence of such configurations is only apparent because of the sensitivity of DCM to single nanotubes, whereas conventional measurements of ensembles are often obscured by sample-to-sample inhomogeneities in size, shape, and orientation.