We solve the crystal structure of recently synthesized cubic BC_{3} using an unbiased swarm structure search, which identifies a highly symmetric BC_{3} phase in the cubic diamond structure (d-BC_{3}) that contains a distinct B-B bonding network along the body diagonals of a large 64-atom unit cell. Simulated x-ray diffraction and Raman peaks of d-BC_{3} are in excellent agreement with experimental data. Calculated stress-strain relations of d-BC_{3} demonstrate its intrinsic superhard nature and reveal intriguing sequential bond-breaking modes that produce superior ductility and extended elasticity, which are unique among superhard solids. The present results establish the first boron carbide in the cubic diamond structure with remarkable properties, and these new findings also provide insights for exploring other covalent solids with complex bonding configurations.