Taking care of resources in cloud computing is fundamental to maintaining required performance and cost objectives, particularly when workloads vary. Conventional methods fail to consider live changes in the system or use resources wisely. To solve these issues, we proposed a new approach we call Optimized Cloud Resource Management based on Deep Dendritic Artificial Neural Networks which are Integrated with Kubernetes and Terraform (CRM-DDANN-KT). The approach starts by collecting performance metrics data from the cloud systems. After collecting the raw data, we clean the data using a Innovative Saturated Koopman Kalman Filter (ISKKF), which removes interference and fills holes in the data. The data is then processed and employed to train a Deep Dendritic Artificial Neural Network (DDANN) model based on how biological neurons are structured. The DDANN returns future requirements for resources in terms of required performance using past behaviors and trends. Predicted performance data from the DDANN then directs the Gazelle Optimization Algorithm (GOA), which captures the required performance and the minimal cost to identify the optimal allocation of resources. Terraform due to its infrastructure as code capabilities translates the decisions of the GOA into monitored and actionable changes to the infrastructure. Kubernetes then responds to the prediction predicted by the GAO, which provides the appropriate scaling to a set of containerized services. Experimental results confirm that CRM-DDANN-KT outperforms the previous methods significantly. Specifically, we achieve a RMSE reduction, respectively, of 52.31%, 64.55% and 57.13% and a MAE reduction of 56.94%, 69.15% and 47.15% against current state-of-the-art methods in the literature. These improvements highlight its ability to adapt to workload shifts while minimizing operational costs. By combining predictive analytics, optimization algorithms, and automation tools, this approach offers a practical solution for dynamic cloud environments.