Ferromagnetic nanomaterials exhibit unique magnetic properties common to materials with dimensions approaching the atomic scale and have potential applications in magnetic data storage. Technological applications, however, require that the detailed magnetic behaviors and configurations of individual and interacting magnetic nano-objects be clarified. We determined the magnetic remnant configurations in single crystalline 30 nm Fe nanocubes and groups of nanocubes using off-axis electron holography in a transmission electron microscope. Our measurements on an isolated cube reveal a vortex state whose core size has been determined. Two neighboring nanocubes with adjacent {100} surfaces exhibit a ferromagnetic dipolar coupling, while similar magnetic interactions between four cubes in a square arrangement induce a bending of the magnetic induction, i.e., a magnetic flux closure state. The various configurations were successfully simulated by micromagnetic calculations.