The increasing prevalence of colon and lung cancer presents a considerable challenge to healthcare systems worldwide, emphasizing the critical necessity for early and accurate diagnosis to enhance patient outcomes. The precision of diagnosis heavily relies on the expertise of histopathologists, constituting a demanding task. The health and well‐being of patients are jeopardized in the absence of adequately trained histopathologists, potentially leading to misdiagnoses, unnecessary treatments, and tests, resulting in the inefficient utilization of healthcare resources. However, with substantial technological advancements, deep learning (DL) has emerged as a potent tool in clinical settings, particularly in the realm of medical imaging. This study leveraged the LC25000 dataset, encompassing 25,000 images of lung and colon tissue, introducing an innovative approach by employing a self‐organized operational neural network (Self‐ONN) to accurately detect lung and colon cancer in histopathology images. Subsequently, our novel model underwent comparison with five pretrained convolutional neural network (CNN) models: MobileNetV2‐SelfMLP, Resnet18‐SelfMLP, DenseNet201‐SelfMLP, InceptionV3‐SelfMLP, and MobileViTv2_200‐SelfMLP, where each multilayer perceptron (MLP) was replaced with Self‐MLP. The models’ performance was meticulously assessed using key metrics such as precision, recall, F1 score, accuracy, and area under the receiver operating characteristic (ROC) curve. The proposed model demonstrated exceptional overall accuracy, precision, sensitivity, F1 score, and specificity, achieving 99.74%, 99.74%, 99.74%, 99.74%, and 99.94%, respectively. This underscores the potential of artificial intelligence (AI) to significantly enhance diagnostic precision within clinical settings, portraying a promising avenue for improving patient care and outcomes. The synopsis of the literature provides a thorough examination of several DL and digital image processing methods used in the identification of cancer, with a primary emphasis on lung and colon cancer. The experiments use the LC25000 dataset, which consists of 25,000 photos, for the purposes of training and testing. Various techniques, such as CNNs, transfer learning, ensemble models, and lightweight DL architectures, have been used to accomplish accurate categorization of cancer tissue. Various investigations regularly show exceptional performance, with accuracy rates ranging from 96.19% to 99.97%. DL models such as EfficientNetV2, DHS‐CapsNet, and CNN‐based architectures such as VGG16 and GoogleNet variations have shown remarkable performance in obtaining high levels of accuracy. In addition, methods such as SSL and lightweight DL models provide encouraging outcomes in effectively managing large datasets. In general, the research emphasizes the efficacy of DL methods in successfully diagnosing cancer from histopathological pictures. It therefore indicates that DL has the potential to greatly improve medical diagnostic techniques.