Correlating the electronic structure and magnetic response with the morphology and crystal structure of the same single ferromagnetic nanoparticle has been up to now an unresolved challenge. Here, we present measurements of the element-specific electronic structure and magnetic response as a function of magnetic field amplitude and orientation for chemically synthesized single Fe nanocubes with 18 nm edge length. Magnetic states and interactions of monomers, dimers, and trimers are analyzed by X-ray photoemission electron microscopy for different particle arrangements. The element-specific electronic structure can be probed and correlated with the changes of magnetic properties. This approach opens new possibilities for a deeper understanding of the collective response of magnetic nanohybrids in multifunctional materials and in nanomagnetic colloidal suspensions used in biomedical and engineering technologies.