There is a trend that the functionalities of communication, computing, and caching (CC&C) are merging together in the future networks. Recently, this mergence is formed by the concept of cloud radio access network (C-RAN) with caching as a service (CaaS). In this paper, we dissect the interactions of CC&C in C-RAN with CaaS from two dimensions: physical resource dimension and time dimension. In the physical resource dimension, we identify how to segment the baseband unit (BBU) pool resources (i.e. computational and storage) into different types of virtual machines (VMs). In the time dimension, we address how the long-term resource segmentation in the BBU pool affects the short-term beamforming in the remote radio heads. We formulate the problem as a stochastic mixed-integer nonlinear programming (SMINLP), and then approximate the problem as a global consensus problem. The alternating direction method of multipliers (ADMM) is utilized to obtain the solution in a distributed fashion. Simulation results demonstrate the that the proposed scheme is more cost saving than that without considering the integration of CC&C.