Single-image super-resolution (SISR) techniques attempt to reconstruct the finer resolution version of a given image from its coarser version. In the SISR of hyperspectral data sets, the simultaneous consideration of spectral bands is crucial for ensuring the spectral fidelity. However, the high spectral resolution of these data sets affects the performance of conventional approaches. This research proposes the design of 3-D convolutional neural network (CNN)-based SISR architectures that can map the spatial-spectral characteristics of hypercubes to a finer spatial resolution. The proposed approaches facilitate the simultaneous optimization of sparse codes and dictionaries with regard to the super-resolution objective. Our main hypothesis is that the consideration of spectral aspects is essential for the spatial enhancement of hyperspectral images. Also, we propose that the regularized deconvolution of a coarser-scale hypercube, using learned 3-D filters, yields the required high-resolution version. Based on these hypotheses, a convolution-deconvolution framework is proposed to super-resolve the hypercubes in parallel with the reconstruction of a set of regularizing features. Novel sparse code optimization sub-networks proposed in this article give better performance than the existing strategies. The endmember similarities and hyperspectral image prior are considered while designing the proposed loss functions. In order to improve the generalizability, a collaborative spectral unmixing strategy is employed to refine the spectral base of the super-resolved result. The spatial-spectral accuracy of the super-resolved hypercubes, in terms of the validity of regularizing features and endmembers, is explored to devise an optimal ensemble strategy. The experiments, over different data sets, confirm better accuracy of the proposed frameworks compared to the prominent approaches.