The current target for expanding the application scope of supercapacitors is to increase their energy density (E) beyond 20 Wh kg−1. In this regard, edge-free carbon materials show considerable potential because of their high working voltage (U) in organic electrolytes; however, their capacitance (C) remains limited. In this study, we synthesized edge-free three-dimensional (3D) graphene materials with different numbers of graphene stacking layers (nstack). These carbon materials have similar pore morphologies and an edge-free structure because a template method and annealing at 1800 °C were applied, respectively. These features allowed C to remain unaffected by the pore size effect, wettability, parasitic side reactions, and pseudocapacitance. Our results suggested that increasing nstack slightly enhances the areal C; however, such an increase cannot compensate for the decrease in C attributed to the decrease in the specific surface area. We also confirmed that the C of 3D graphene materials has a quantum origin, which results in a “butterfly shaped” cyclic voltammetry curve; we also successfully quantified the quantum capacitance (CQ) for the complete understanding of the origin of C. Based on this knowledge, we estimated that this 3D graphene material can yield a high E of 43 Wh kg−1 once CQ is optimized.