Recent progress in nanoscale self-assembly has led to the realization of 3D nanostructures with unique optoelectronic properties through a surface tension driven self-folding of diverse 2D graphene patterns. The self-assembly of 2D patterned graphene can yield 3D micro/nanoscale polyhedrons such as closed and open cubic structures with free-standing 2D materials (graphene or graphene oxide) acting as faces of the cube. Self-assembly is a versatile technique that can realize 3D graphene cubes of dimensions ranging from 100 nm to 200 µm. Here, we present simulation and measurement results to study of the optical properties of nanocubes at their plasmon resonance as well as the off-resonance broadband properties of the micro and nanoscale graphene cubes. At a nanoscale, the uniform plasmon coupling in 3D graphene nanocubes gives rise to hybridized modes with strong enhancement of the incident electric (E)-field. The hybrid modes demonstrate large area hotspots of constant field enhancement with a much slower decay of the field away from the surface, giving rise to a volumetric field that is 2 orders of magnitude stronger than that in 2D ribbons. Moreover, even in the absence of plasmon resonance such as in 200 µm sized 3D graphene cubes, the rippled geometry induces a strong absorbance of 2-40% over the entire measured wavelength of 1-10 µm. Fourier transform infrared (FTIR) spectroscopy of the 3D graphene microcubes and Comsol Multiphysics simulations reveal that the angle of incidence, number of graphene layers, and the ripple geometry can be modified to tune the absorbance in 3D graphene over a wider range than in 2D graphene. Thus, the 3D free-standing graphene cubes offer an opportunity to overcome the weak ~3% broadband absorption in 2D planar graphene. The highly confined volumetric field within the nanocubes and strong tunable absorption in graphene microcubes provide an opportunity for the development of non-contact ultrasensitive 3D plasmonic sensors and devices with a larger active area and higher efficiency.