5G and 6G represent next‐generation communication technologies that provide high spectral and energy efficiency, low latency, and massive connectivity due to extensive growth in Internet‐of‐Things devices. Their impact on the quality of life will be significant and enable them to shape modern society's future. The intensive network softwarization and cloudification represent leading drivers for future core network development. Therefore, educational institutions must respond quickly and ensure these technologies' easy and rapid adoption. It is necessary to introduce new approaches to engineers' education, shifting the focus from traditional network technologies toward more programmable network concepts based on network softwarization and cloudification. Our research goal has been to develop and implement a course while focusing on conceiving technical and pedagogical solutions to provide high‐quality education. We have used globally available APIs, tools, and open‐source software to achieve deeper student involvement in our course. We have evaluated our approach by surveying students at the School of Computing, Union University of Belgrade. The results indicate students' high satisfaction with the proposed course. At the same time, they reveal specific problems that affect the effective acceptance of knowledge from certain areas covered in the course. Finally, we have prepared a list of guidelines for teaching courses of 5G/6G core.