The presence of cortical lesions in multiple sclerosis patients has emerged as an important biomarker of the disease. They appear in the earliest stages of the illness and have been shown to correlate with the severity of clinical symptoms. However, cortical lesions are hardly visible in conventional magnetic resonance imaging (MRI) at 3T, and thus their automated detection has been so far little explored. In this study, we propose a fully-convolutional deep learning approach, based on the 3D U-Net, for the automated segmentation of cortical and white matter lesions at 3T. For this purpose, we consider a clinically plausible MRI setting consisting of two MRI contrasts only: one conventional T2-weighted sequence (FLAIR), and one specialized T1-weighted sequence (MP2RAGE). We include 90 patients from two different centers with a total of 728 and 3856 gray and white matter lesions, respectively. We show that two reference methods developed for white matter lesion segmentation are inadequate to detect small cortical lesions, whereas our proposed framework is able to achieve a detection rate of 76% for both cortical and white matter lesions with a false positive rate of 29% in comparison to manual segmentation. Further results suggest that our framework generalizes well for both types of lesion in subjects acquired in two hospitals with different scanners.