In this paper, we investigate robust energy efficiency design for multicast downlink cloud radio access network (C- RAN) for both data-sharing and compression strategies. The two strategies mainly differ in whether the baseband units pool compresses the user messages before transmitting them to remote radio heads (RRH). The performance of worst-case energy efficiency for both strategies is compared by formulating the robust energy efficiency maximization problem subjected to finite RRH power budgets, limited fronthaul link capacity, and minimum quality-of-service constraints when only imperfect channel state information (CSI) is available at the transmitter. To solve these problems, we cast them into semidefinite program problems and solve them iteratively. Simulation results demon- strate effectiveness of our proposed algorithms and two strategies are compared under imperfect CSI.