In peripheral collisions, the strong electromagnetic fields are produced since the fully stripped heavy ions moves at ultra-relativistic velocities. Lepton pairs, especially the electron-positron pairs are the result of this collisions. At the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC), virtual photons produce many particles such as electron-positron pairs, heavy lepton (muons and tauons) pairs, magnetic monopoles, W-pairs, b-quark pairs and possibly the Higgs. At small impact parameters, the colliding nuclei make peripheral collisions, photon fluxes are very large and these are responsible for the multiple photonuclear interactions. Free pair productions, bound free pair productions, and nuclear Coulomb excitations are important examples of such interactions, and these processes play important roles in the beam luminosity at RHIC and LHC. Here we obtained bound free electron-positron pair production with nuclear breakup for heavy ion collisions at RHIC and LHC.