Cloud computing platforms can be highly attractive to conduct course assignments and empower students with valuable and indispensable hands-on experience. In particular, the cloud can offer teaching staff and students (whether local or remote) on-demand, elastic, dedicated, isolated, (virtually) unlimited, and easily configurable virtual machines. As such, employing cloud-based laboratories can have clear advantages over using classical ones, which impose major hindrances against fulfilling pedagogical objectives and do not scale well when the number of students and distant university campuses grows up. We show how the cloud paradigm can be leveraged to teach a cybersecurity course. Specifically, we share our experience when using cloud computing to teach a senior course on cybersecurity across two campuses via a virtual classroom equipped with live audio and video. Furthermore, based on this teaching experience, we propose guidelines that can be applied to teach similar computer science and engineering courses. We demonstrate how cloud-based laboratory exercises can greatly help students in acquiring crucial cybersecurity skills as well as cloud computing ones, which are in high demand nowadays. The cloud we used for this course was the Amazon Web Services (AWS) public cloud. However, our presented use cases and approaches are equally applicable to other available cloud platforms such as Rackspace and Google Compute Engine, among others.