Self-supervised learning (SSL) has advanced medical image analysis be enabling learning form large unlabelled data. However, in brain magnetic resonance imaging (MRI), most 3D models remain specialized for either segmentation of classification, limiting their ability to generalize across datasets, imaging protocols,, and downstream tasks. This lack of transferability constrains the clinical utility of 3D MRI models, despite the availability of unlabeled volumetric data. We present Volta-3D, a self-supervised 3D Vision Transformer framework designed to learn transferable volumetric representations. Volta-3D jointly aligns global class-style tokens and local patch tokens within a student-teacher paradigm and enforces fine-grained structural reconstruction. This combined global-local alignment addresses the limited semantic diversity and subtle anatomical characteristics of brain MRI, which challenges existing SSL approaches. We evaluate Volta-3D on multiple out-of-distribution downstream tasks, including hippocampal segmentation and classification of sex and Alzheimer's disease versus healthy controls. Across all tasks, representations learned by Volta-3D outperform randomly initialized baselines, demonstrating improved transferability and robustness under domain shift. Hence jointly enforcing global semantic consistency and local structural learning during pretraining enables broader concept learning from unlabeled brain MRI data. Overall VolTA-3D supports effective multi-task downstream performance with task-specific pertaining, a step towards generalizable and clinically viable 3D models.