Exploiting cognition to the cache-enabled device-to-device (D2D) communication underlaying the multi-channel cellular network is the main focus of this paper. D2D pairs perform direct communications via sensing the available cellular channels, bypassing the base station (BS). Dynamic service is considered and the network performance is evaluated with the stochastic geometry. Node locations are first modeled as mutually independent Poisson Point Processes, and the service queueing process is formulated. Then the corresponding tier association and cognitive access protocol are developed. The delay and the length for the queue at the BS and D2D transmitter are further elaborated, with modeling the traffic dynamics of request arrivals and departures as the discrete-time multiserver queue with priorities. Moreover, impacts of the physical layer and content-centric features on the system performance are jointly investigated to provide a valuable insight.