The capacity region of the Multicast Cognitive Interference Channel (CIFC) is investigated. This channel consists of two independent transmitters that wish to multicast two different messages, each of them to a different set of users. In addition, one of the transmitters --commonly referred to as the cognitive transmitter-- has prior non-causal knowledge of both messages to be transmitted. This scenario combines difficulties and challenges arising in the Interference Channel, the Broadcast Channel and multicasting communications. Our aim concerns the derivation of optimal interference mitigation techniques in such a challenging communication setup. We investigate to this end the multi-primary CIFC and its dual multi-secondary CIFC under various interference regimes as an attempt to build a thorough understanding for the more general setting. It is shown that, for some regimes, well-known coding techniques for the conventional CIFC remain still optimal in the presence of multicasting. While in other regimes, evolved encoding and/or decoding strategies are crucial. A careful use of these coding schemes and new outer bounding techniques allows us to characterize the capacity region for several classes of discrete memoryless and Gaussian channels in different interference regimes.