Here we present our arguments for a more in-depth study of the Boolean cube, which is one of the most important discrete structures. The article contains a case study that analyses how the Boolean cube has been included and explained in more than 80 different sources. However, organized material on the Boolean cube is lacking. We examine and show why the topic of the Boolean cube deserves to be studied in the course on Discrete Structures -- a basic part of the Computer Science curriculum. The benefits of mastering such knowledge and programming skills are pointed out. A sample lecture on the $n$-dimensional Boolean cube (including selected exercises, their answers, hints or solutions) is developed and discussed. It introduces, generalizes and relates many concepts from different subjects in the area of Discrete Mathematics and outside it. So the lecturers can use the sample lecture when teaching those subjects. In this way, all these concepts become more understandable, applicable and useful to the students. The lecture can be taught in a form of presentation or given to the students for "Online self-learning", in order to write homework, or develop a course project related to the topic, etc. All supporting resources to the lecture are available for free use at \cite{VB_Lect}.