Current graphene-based plasmonic devices are restricted to 2D patterns defined on planar substrates; thus, they suffer from spatially limited 2D plasmon fields. Here, 3D graphene forming freestanding nanocylinders realized by a plasma-triggered self-assembly process are introduced. The graphene-based nanocylinders induce hybridized edge (in-plane) and radial (out-of-plane) coupled 3D plasmon modes stemming from their curvature, resulting in a four orders of magnitude stronger field at the openings of the cylinders than in rectangular 2D graphene ribbons. For the characterization of the 3D plasmon modes, synchrotron nanospectroscopy measurements are performed, which provides the evidence of preservation of the hybridized 3D graphene plasmons in the high precision curved nanocylinders. The distinct 3D modes introduced in this paper, provide an insight into geometry-dependent 3D coupled plasmon modes and their ability to achieve non-surface-limited (volumetric) field enhancements.