Unique multicenter bonding in boron-rich materials leads to the formation of complex structures and intriguing properties. Here global structural searches are performed to unearth the structure of beryllium hexaboride (BeB6) synthesized decades ago. Three BeB6 phases (α, β, and γ) were predicted to be stable at ambient and high pressures. The ground state at ambient pressure, α-BeB6, consists of a strong and uniformly distributed covalent B-B network, which results in exceptional elastic properties and a hardness of 46 GPa comparable to γ-B. Even more surprisingly, α-BeB6 retains credible electron phonon coupling in the boron sublattice, and is predicted to be superconducting at 9 K. Above 4 GPa, β-BeB6 is stabilized with alternating boron slabs and triangular beryllium layers analogous to the structure of MgB2. The β-BeB6 is predicted to be superconducting at 24 K, similar to Nb3(Al,Ge). The γ-BeB6 is stable above 340 GPa. The understanding of intrinsic multicenter-bonding mechanism and related properties demonstrated in the very example of BeB6 provides new insights for the design of tunable multifunctional materials.