Cloud computing has emerged as a popular technologies which provide on-demand services to the end users. Such services are hosted by massive geo-distributed data centers(DCs). Nowadays, connected vehicles in a smart city can also avail cloud services through Internet using cellular technologies. But, the advent of 5G technology has posed challenges for DCs such as-low latency and higher data rate requirements. To handle these challenges, edge-DCs(EDCs) can be deployed across a smart city to provide low latency services to the connected vehicles. In lieu of this, in this paper, EDCSuS: Sustainable EDC as a service framework in software defined vehicular environment is proposed. In EDCSuS, firstly, a software defined controller handles the incoming requests and suggest an optimal flow path. Secondly, a multi-leader multi-follower Stackelberg game is presented for resource allocation. Thirdly, to improve the resource utilization, a cooperative resource sharing scheme is designed, thereby minimizing the energy consumption of servers in the EDCs. Lastly, a caching scheme is presented to avert excessive energy consumption for retracing the lost link due to vehicular mobility. The efficacy of the proposed scheme has been evaluated using extensive simulations with respect to various parameters. The results obtained prove the effectiveness of EDCSuS.