Fully relativistic calculations, primarily at the 4-component coupled-cluster singles and doubles with perturbative triples [CCSD(T)] level of theory with the Dirac-Coulomb (DC) Hamiltonian, have been carried out for the superheavy (E125)F molecule using large Gaussian basis sets. The electronic ground state is determined to have an [Og]8s25g16f3 configuration on E125 with an Ω = 6 ground state and an 8p electron largely donated to F. A Mulliken population analysis indicates that the ground state is mainly ionic with a partial charge of +0.79 on E125 and a single sigma bond involving the F 2p and E125 8p spinors. The occupied g spinor is not involved in the bonding. With the largest basis set used in this work, the (0K) dissociation energy was calculated at the DC-CCSD(T) level of theory to be 7.02eV. Analogous calculations were also carried out for the E125 atom, both the neutral and its cation. The lowest energy electron configuration of E125+, [Og]8s1/225g7/216f5/23 with a J = 6 ground state, was found to be similar to that in (E125)F, while the neutral E125 atom has an [Og]8s1/225g7/216f5/227d3/218p1/21 ground state electron configuration with a J = 17/2 ground state. The ionization energy (IE) of E125 is reported for the first time and is calculated to be 4.70eV at the DC-CCSD(T) level of theory. Non-relativistic calculations were also carried out on the E125 atom and the (E125)F molecule. The non-relativistic ground state of the E125 atom was calculated to have a 5g5 ground state with an IE of just 3.4eV. The net effect of relativity on (E125)F is to stabilize its bonding.