Super-resolution (SR) aims to increase the resolution of imagery. Applications include security, medical imaging, and object recognition. We propose a deep learning-based SR system that takes a hexagonally sampled low-resolution image as an input and generates a rectangularly sampled SR image as an output. For training and testing, we use a realistic observation model that includes optical degradation from diffraction and sensor degradation from detector integration. Our SR approach first uses nonuniform interpolation to partially upsample the observed hexagonal imagery and convert it to a rectangular grid. We then leverage a state-of-the-art convolutional neural network architecture designed for SR known as residual channel attention network (RCAN). In particular, we use RCAN to further upsample and restore the imagery to produce the final SR image estimate. We demonstrate that this system is superior to applying RCAN directly to rectangularly sampled LR imagery with equivalent sample density. The theoretical advantages of hexagonal sampling are well known. However, to the best of our knowledge, the practical benefit of hexagonal sampling in light of modern processing techniques such as RCAN SR is heretofore untested. Our SR system demonstrates a notable advantage of hexagonally sampled imagery when employing a modified RCAN for hexagonal SR.