Cloud-RAN is a key 5G enabler; it centralizes the baseband processing of several base stations by executing the baseband functions in a centralized, virtualized, and shared entity known as the Base Band Unit (BBU)-Pool. Cloud-RAN paves the way for joint management of the radio and computing resources of multiple base stations. In fact, centralization and virtualization allow for decreasing energy consumption which decreases Capital Expenditure (CAPEX) and Operational Expenditure (OPEX). Cloud-RAN architecture permits jointly allocating the radio and computing resources of multiple base stations. The radio resources include the Resource Blocks (RBs), the transmission power, and the Modulation Coding Scheme (MCS), whereas the computing resources include the CPUs resources. This paper investigates the potential benefits that could be scored thanks to the joint allocation of these two types of resources, with respect to energy consumption and overall throughput, when radio resources are finite and computing resources are not. The latter is an effect of the C-RAN architecture, which allows scalability and fast computing resource provisioning. Due to the unconstrained availability of computing resources, the joint allocation of radio and computing resources has a negligible impact when the objective is throughput maximization. However, it is highly beneficial when the target is energy consumption minimization in comparison to the sequential allocation that consists of allocating radio resources first, and then computing resources are allocated. For that, we formulate a Mixed Integer Linear Programming (MILP) problem having the objective of minimizing energy consumption. When the goal is to minimize energy consumption, the joint allocation of radio and computing resources reduces the total energy consumption by up to 21.3% when compared to the case where radio and computing resources in the BBU pool are allocated sequentially. Furthermore, given the NP-hardness of solving a MILP problem, we propose a two-step low-complexity matching game-based algorithm with a transmission power adjustment mechanism that aims at performing close to the MILP solver. The results show that our proposed matching game algorithm is a good alternative for solving the joint-allocation MILP problem, producing results that are very close to the MILP optimal solutions.