In this paper, a cloud radio access network (C-RAN) is considered where the remote radio heads (RRHs) are separated from the baseband units which form a common pool of computational resource units. Depending on their capacity, the RRHs may form one or more clusters. Each RRH accommodates multiservice traffic, i.e., calls from different service-classes with different radio and computational resource requirements. Arriving calls follow a Poisson process and simultaneously require radio and computational resource units in order to be accepted in the serving RRH. If their resource requirements cannot be met then calls are blocked and lost. Otherwise, calls remain in the serving RRH for a generally distributed service time. Assuming the single-cluster C-RAN, we model it as a multiservice loss system, prove that a product form solution exists for the steady-state probabilities and determine call blocking probabilities via an efficient convolution algorithm whose accuracy is validated via simulation. Furthermore, we generalize the previous multiservice loss model by considering the more complex multi-cluster case where RRHs of the same capacity are grouped in different clusters.