Spectrum sensing is a key technique for dynamically detecting available spectrum in cognitive radio networks (CRNs), which can introduce high resource demands such as energy consumption. In this paper, we propose a novel cluster-based cooperative sensing-after-prediction scheme where a learning cluster and a sensing cluster are jointly considered to perform cooperative prediction and sensing efficiently. This enables us to skip the complex physical sensing to reduce the demands when the spectrum availability can be simply predicted using cooperative prediction. Furthermore, the clustering is flexible, in order to meet different performance requirements. We then formulate two optimization problems to minimize the total number of users in the two clusters or to minimize the total energy consumption, to meet different performance requirements, while in both cases guaranteeing the system accuracy requirement and individual energy constraints. To solve the two challenging integer programming problems, the unconstrained problems are mathematically solved first by relaxing the integer variable and fixing the cluster size. Such analytical solutions serve as a foundation for solving the original optimization problems. Then, two low-complexity search algorithms are proposed to achieve the global optimum, as they can obtain the same performance with exhaustive search. Simulation results validate the accuracy of the derived analytical expressions and demonstrate that the total energy consumption and the number of users contributing to learning and sensing can be greatly reduced by applying our optimized clustered sensing-after-prediction scheme.