Development of robust general purpose 3D segmentation frameworks using the latest deep learning techniques is one of the active topics in various bio-medical domains. In this work, we introduce Temporal Cubic PatchGAN (TCuP-GAN), a volume-to-volume translational model that marries the concepts of a generative feature learning framework with Convolutional Long Short-Term Memory Networks (LSTMs), for the task of 3D segmentation. We demonstrate the capabilities of our TCuP-GAN on the data from four segmentation challenges (Adult Glioma, Meningioma, Pediatric Tumors, and Sub-Saharan Africa subset) featured within the 2023 Brain Tumor Segmentation (BraTS) Challenge and quantify its performance using LesionWise Dice similarity and 95% Hausdorff Distance metrics. We demonstrate the successful learning of our framework to predict robust multi-class segmentation masks across all the challenges. This benchmarking work serves as a stepping stone for future efforts towards applying TCuP-GAN on other multi-class tasks such as multi-organelle segmentation in electron microscopy imaging.