[3] In addition to his participation in basketball at a young age, Cockburn also played soccer, cricket, and ran in track and field.

[5] During the summer of 2018 on the Nike Elite Youth Basketball League (EYBL) circuit with the NY Rens, Cockburn averaged 16.3 points and 10.3 rebounds per game, while shooting 53.9 percent from the field.

[6] Prior to his junior year, Cockburn was selected to participate in the 2017 Basketball Without Borders Americas camp that was held in Nassau, Bahamas.

[8] For his senior season, Cockburn transferred to Oak Hill Academy in Mouth of Wilson, Virginia, where he was teammates with fellow five-star recruits Cole Anthony and Cameron Thomas.

[9] Prior to his senior high school season at Oak Hill Academy, Cockburn held 26 scholarship offers and narrowed the list of schools he was considering to 12, which included Cincinnati, Florida State, Illinois, Kansas, Kentucky, LSU, Oregon, Pittsburgh, South Carolina, St. John's, Syracuse and UConn.

[15] Cockburn was named Big Ten player of the week on 25 November after setting a school freshman record for rebounds in a game with 17 to go along with 18 points in a win versus The Citadel.

[16] On 11 December 2020, Cockburn had 19 points, 10 rebounds and four blocks in a 71–62 victory over fifth-ranked Michigan, Illinois' first win over a top-five program since 2013.

[28] On 20 June 2023, Cockburn signed with the Seoul Samsung Thunders of the Korean Basketball League (KBL).