Skin cancer is one of the deadliest kinds of cancer because of it’s due to its visible onset and the potential for rapid progression and spread. Oncologists employ several techniques, including imaging and biopsies, to determine whether skin cancer is present, but these are labor-intensive and time-consuming. Developing an automated and accurate framework is essential for early skin cancer detection, which greatly increases the probability of a successful treatment and recovery. Therefore, to address the aforementioned problems, this study aim to propose a novel Deep Learning (DL)-based multi-class skin cancer classification (MC-SC2) model for automatically diagnosing skin cancers using dermoscopic images. Initially, the dermoscopic images are preprocessed using a Gaussian Filter (GF) to effectively remove noise. To address the class imbalance issue, we applied advanced augmentation techniques to oversample minority classes, ensuring a uniform class distribution and enhancing the model's ability to generalize. To extract the complex and dominant features, we propose a novel DL-based model called BAM-EfficientNet (Bottleneck Attention Module with EfficientNetB7). In BAM-EfficientNet, we replace each Squeeze-and-Excitation (SE) attention module with a BAM in the traditional EfficientNetB7; this modification enables the network to concentrate on the most relevant regions in the images. The extracted features fed into the proposed Modified Stacked Capsule Network (MSCNet) to classify a skin lesion image as AKIEC, BCC, BKL, DF, MEL, NV, and VASC. In the proposed MSCNet employs the Disperse Dynamic Routing (DDR) algorithm to improve capsule networks performance, and network's initial weights and biases are fine-tuned using Pelican Optimization Algorithm (POA) to further enhance performance. The HAM10000 dataset is used to assess the suggested model. The findings indicate that our approach beats current methods with an accuracy of 99.21% in classifying the seven different types of skin cancer, yielding substantial outcomes. These results demonstrate the potential of the suggested model as a quick, precise, and useful tool for early skin cancer diagnosis, providing important assistance in diagnosing skin cancer for medical professionals.