Advancements in EEG biometric technologies have been hindered by two persistent challenges: the management of large data sizes and the unreliability of data resulting from various measurement environments. Addressing these challenges, this study introduces a novel methodology termed 'Cube-Code' for cognitive biometric authentication. As a preliminary step, Automatic Artifact Removal (AAR) leveraging wavelet Independent Component Analysis (wICA) is applied to EEG signals. This step transforms the signals into independent sub-components, effectively eliminating the effects of muscle movements and eye blinking. Subsequently, unique 3-Dimensional (3-D) Cube-Codes are generated, each representing an individual subject in the database. Each Cube-Code is constructed by stacking the alpha, beta, and theta sub-band partitions, obtained from each channel during each task, back-to-back. This forms a third-order tensor. The stacking of these three subbands within a Cube-Code not only prevents a dimension increase through concatenation but also permits the direct utilization of non-stationary data, bypassing the need for fiducial component detection. Higher-Order Singular Value Decomposition (HOSVD) is then applied to perform a subspace analysis on each Cube-Code, an approach supported by previous literature concerning its effectiveness on 3-D tensors. Upon completion of the decomposition process, a flattening operation is executed to extract lower-dimensional, taskindependent feature matrices for each subject. These feature matrices are then employed in five distinct deep learning architectures. The Cube-Code methodology was tested on EEG signals, composed of different tasks, from the PhysioNet EEG Motor Movement/Imagery (EEGMMI) dataset. The results demonstrate an authentication accuracy rate of approximately 98%. In conclusion, the novel Cube-Code methodology provides highly accurate results for subject recognition, delivering a new level of reliability in EEG-based biometric authentication.