Human pose estimation is considered one of the major challenges in the field of Computer Vision, playing an integral role in a large variety of technology domains. While, in the last few years, there has been an increased number of research approaches towards CNN-based 2D human pose estimation from RGB images, respective work on CNN-based 3D human pose estimation from depth/3D data has been rather limited, with current approaches failing to outperform earlier methods, partially due to the utilization of depth maps as simple 2D single-channel images, instead of an actual 3D world representation. In order to overcome this limitation, and taking into consideration recent advances in 3D detection tasks of similar nature, we propose a novel fully-convolutional, detection-based 3D-CNN architecture for 3D human pose estimation from 3D data. The architecture follows the sequential network architecture paradigm, generating per-voxel likelihood maps for each human joint, from a 3D voxel-grid input, and is extended, through a bottom-up approach, towards multi-person 3D pose estimation, allowing the algorithm to simultaneously estimate multiple human poses, without its runtime complexity being affected by the number of people within the scene. The proposed multi-person architecture, which is the first within the scope of 3D human pose estimation, is comparatively evaluated on three single person public datasets, achieving state-of-the-art performance, as well as on a public multi-person dataset achieving high recognition accuracy.