Extending the capabilities of electron tomography with advanced imaging techniques and novel data processing methods, can augment the information content in three-dimensional (3D) reconstructions from projections taken in the transmission electron microscope (TEM). In this work we present the application of simultaneous electron energy-loss spectroscopy (EELS) and energy-dispersive X-ray spectroscopy (EDS) to scanning TEM tomography. Various tools, including refined tilt alignment procedures, multivariate statistical analysis and total-variation minimization enable the 3D reconstruction of analytical tomograms, providing 3D analytical metrics of materials science samples at the nanometer scale. This includes volumetric elemental maps, and reconstructions of EDS, low-loss and core-loss EELS spectra as four-dimensional spectrum volumes containing 3D local voxel spectra. From these spectra, compositional, 3D localized elemental analysis becomes possible opening the pathway to 3D nanoscale elemental quantification.