Brain cancer's severity necessitates precise brain tumor segmentation, which is crucial for effective brain tumor diagnosis. Manual identification, burdened by high costs, labor, and error risks, highlights the need for automated methods. In this study, we introduce the Global Context-aware Squeeze and Excite Residual UNet (GCSER-UNet), which facilitates a fusion of spatial and channel-wise attention and thus enhances the model's capacity to capture intricate spatial dependencies and contextual information. GCSER-UNet efficiently extracts tumor segments from multimodal MRI slices, delivering exceptional performance. Evaluations on benchmark databases exhibit its superiority, achieving a notable 94 percent dice score on the TCGA LGG dataset, surpassing the state-of-the-art dice score of 91.8 percent. In the BraTS 2020 dataset, the proposed GCSER-UNet ensemble approach yielded dice scores of 95 percent, 92 percent, and 90 percent for the tumor regions - Whole Tumor (W), Tumor Core (T), and Enhancing Tumor (E), respectively. The current state-of-the-art dice scores were 94 percent, 93 percent, and 88 percent. These compelling outcomes highlight the efficacy of GCSER-UNet in precise brain tumor segmentation and thus can aid neurologists in effective brain cancer management and treatment planning.