Elastic optical networks (EONs) and space-division multiplexing (SDM) have emerged as a promising technology to accommodate the high-capacity and dynamic bandwidth demands of nextgeneration network. However, the problems of high energy consumption and inter-core crosstalk (ICXT) in space-division multiplexing elastic optical networks (SDM-EONs) are also particularly prominent. In this paper, we proposed an energy efficient grooming and hybrid crosstalk solution (EEG-HCS) algorithm. Firstly, in the routing strategy, a candidate path sorting formula combined the path length and path load state is designed to select the candidate paths and balance the network load. According to the sorting result, whether the current candidate path satisfied the energy efficiency grooming condition or not is determined. When the candidate path meet the energy efficiency grooming condition, the energy efficiency grooming algorithm is used to reduce the transmission energy consumption. For traffic request that do not satisfied the grooming condition, a new optical path is established. Through the core priority grouping, combined with crosstalk avoidance strategy and ICXT aware algorithm, the impact of inter-core crosstalk is minimized, and the probability of successful transmission is improved. In order to evaluate the performance of proposed algorithm, ICXT improvement index is defined. The simulation results show that the proposed algorithm can significantly reduce the energy consumption of space-division multiplexing elastic optical network system while ensuring the optimal blocking probability performance.