Cluster computation has been used in the applications that demand performance, reliability, and availability, such as cluster server groups, large-scale scientific computations, distributed databases, distributed media-on-demand servers and search engines etc. In those applications, multicast can play the vital roles for the information dissemination among groups of servers and users. This paper proposes a set of novel efficient fault-tolerant multicast routing algorithms on hypercube interconnection of cluster computers using multicast shared tree approach. We present some new algorithms for selecting an optimal core (root) and constructing the shared tree so as to minimize the average delay for multicast messages. Simulation results indicate that our algorithms are efficient in the senses of short end-to-end average delay, load balance and less resource utilizations over hypercube cluster interconnection networks.