We study structural and electronic properties of graphene grown on SiC substrate using scanning tunneling microscope (STM), spot-profile-analysis low energy electron diffraction (SPA-LEED) and angle resolved photoemission spectroscopy (ARPES). We find several new replicas of Dirac cones in the Brillouin zone (BZ). Their locations can be understood in terms of combination of basis vectors linked to SiC 6x6 and graphene 6xsqrt(3) x 6sqrt(3) reconstruction. Therefore these new features originate from the Moie caused by the lattice mismatch between SiC and graphene. More specifically, Dirac cones replicas are caused by underlying weak modulation of the ionic potential by the substrate that is then experienced by the electrons in the graphene. We also demonstrate that this effect is equally strong in single and tri-layer graphene, therefore the additional Dirac cones are intrinsic features rather than result of photoelectron diffraction. These new features in the electronic structure are very important for the interpretation of recent transport measurements and can assist in tuning the properties of graphene for practical applications.