The recent rapid advancement of cloud-native networking infrastructure has leveraged the resource virtualization technology of containers to realize diverse microservice-based applications in 5G/6G networks and clouds. Containers drastically enhance the efficiency of computational resource allocation and utilization as compared to the related virtualization technology of Virtual Machines (VMs). The networking environment leveraging both VM and container mixed virtualization technologies makes the most use of them to realize a computational platform whose resources can be dynamically adjusted to a fine granularity. To continuously meet the required levels of quality of services in 5G/6G networks and clouds in that platform, an agile and autonomous data analytics system in the control plane is essential for the accurate prediction of server workloads and dynamic allocation of enough amount of computational resource. In this paper, we introduce a framework, which complies with Recommendation ITU-T Y.3177, for autonomous computational resource control and management. The framework consists of an advanced data analytics system and a resource control system. We propose an architecture for the advanced data analytics system consisting of learning and prediction components. The learning component includes a three-stage intelligent model pipelining with three cascaded machine learning models, nonlinear regression, clustering, and multiple regression. These models determine the fluctuation trends in CPU utilization, classify services with similarities in the trends, and predict the peak CPU utilization of each containerized microservice. We evaluate the proposed models through experiments and numerical analysis. The results prove that the models support agile data analytics, which can complete data processing in the time granularity of seconds and achieve higher prediction accuracy of CPU utilization.