The term for a male friendship that is so close that they are like brothers is often called a "brotherly" or "brother-like" friendship. In some cases, you might also hear it referred to as a "bromance." The word "bromance" is a blend of "brother" and "romance," but it doesn't imply a romantic relationship. Instead, it highlights the strong emotional bond and camaraderie between two male friends who share a deep and affectionate connection, much like brothers.