Based on the parameters from published ab-inito theoretical and experimental studies, and combining Molecular Dynamics (MD) and kinetic Monte Carlo (KMC) simulations, a framework of multi-scale modeling is developed to investigate the long-term evolution of displacement damage induced by heavy-ion irradiation in cubic silicon carbide. The isochronal annealing after heavy ion irradiation is simulated, and the annealing behaviors of total interstitials are found consistent with previous experiments. Two annealing stages below 600K and one stage above 900K are identified. The mechanisms for those recovery stages are interpreted by the evolution of defects. The influence of the spatial correlation in primary damage on defect recovery has been studied and found insignificant when the damage dose is high enough, which sheds light on the applicability of approaches with mean-field approximation to the long-term evolution of damage by heavy ions in SiC.