Data augmentation techniques are pivotal in enhancing the generalization capabilities of deep artificial neural networks. Traditional approaches in image augmentation often prioritize generating samples comprehensible to human observers, inadvertently overlooking a spectrum of data potentially beneficial for neural network training. This paper introduces a novel data augmentation technique for image classification tasks, termed Sum Augmentation, which expands upon the concept of linear interpolation of inputs. Our method distinctively combines a substantially larger number of data points, substantially expanding the dataset size. We demonstrate the utility of generating up to eight combined samples to produce complex images, which, though seemingly unintelligible, enable deep models to extract valuable insights. We propose Cascading Sum Augmentation, a novel training procedure that effectively transfers this knowledge, enhancing model generalization. Our findings indicate a more pronounced accuracy improvement in smaller datasets. We also introduce a derived test-time augmentation technique from Sum Augmentation to further boost performance.