In the framework of static and QCD-motivated model potentials for heavy quarkonium, we present a further comprehensive calculation of the mass spectrum of  system and its ground state spin-dependent splittings in the context of the shifted l-expansion technique. We also predict the leptonic constant f_Bc of the lightest pseudoscalar B_c, and  of the vector  states taking into account the one-loop and two-loop QCD corrections. Furthermore, we use the scaling relation to predict the leptonic constant of the nS-states of the  system. Our predicted results are generally in high agreement with some earlier numerical methods. The parameters of each potential are adjusted to obtain best agreement with the experimental spin-averaged data (SAD).