Cadogan joined the Douglas club at a young age and played in all grades at juvenile and underage levels. He enjoyed championship success in the under-14 and under-16 grades.[citation needed]
On 11 June 2011, Cadogan made his senior championship debut for Douglas when he came on as a 54th-minute substitute in a 0-09 to 1-14 defeat by Blackrock in the Cork Senior Championship.[1]
Cork
Minor and under-21
Cadogan first played for Cork as a dual player at minor level. He made his first appearance for the Cork minor football team on 13 April 2011 in a 2-10 to 0-11 defeat of Clare in the Munster Championship.[2] Cadogan made his debut with the Cork minor hurling team two weeks later in a 2-14 to 0-12 defeat by Limerick in the Munster Championship.[3] On 3 July, he was at left corner-forward when the Cork minor football team suffered a 3-11 to 1-09 defeat by Tipperary in the Munster final.[4]
On 11 April 2012, Cadogan made his first appearance for the Cork under-21 football team. He came on as a substitute for Mark Sugrue in the 2-12 to 1-14 Munster Championship final defeat of Kerry.[5]
On 9 April 2011, Cadogan won his second Munster Championship medal when the Cork under-21 football team defeated Tipperary by 1-17 to 0-09 in the final.[6] On 4 May, he scored a point from right wing-forward when Cork suffered a 1-14 to 1-11 defeat by Galway in the All-Ireland final.[7] Cadogan became a dual player in the under-21 grade on 17 July when he lined out for the Cork under-21 hurling team in their 5-19 to 2-13 defeat by Tipperary in the Munster Championship.[8]
Cadogan won a third successive Munster Championship medal with the Cork under-21 football team on 9 April 2014 when he scored five points from play in the 1-18 to 3-08 defeat of Tipperary in the final.[9] On 30 July, he was held scoreless at full-forward when the Cork under-21 hurling team suffered a 1-28 to 1-13 defeat by Clare in the Munster Championship final.[10]
Senior
Cadogan made his first appearance for the Cork senior hurling team on 15 February 2014 in a 0-17 apiece draw with Limerick in the National Hurling League.[11] He was later included on Cork's panel for the 2014 Munster Championship and made his debut on 25 May in a 1-21 apiece draw with Waterford, in which he was also named man of the match.[12] On 3 July, Cadogan won a Munster Championship medal after scoring four points in Cork's 2-24 to 0-24 defeat of Limerick in the last final to be played at the old Páirc Uí Chaoimh.[13] He ended the season by being nominated for an All-Star.[14]
On 3 May 2015, Cadogan was at right corner-forward in Cork's 1-24 to 0-17 defeat by Waterford in the National League final.[15]
Cadogan won his second Munster Championship medal on 9 July 2017 after scoring 1-04 from play in the 1-25 to 1-20 defeat of Clare in the final.[16] He ended the season by securing a second All-Star nomination.[17]
On 24 May 2018, it was reported that Cadogan would miss the Munster Championship after he underwent surgery on his knee the previous week.[18] He returned to the extended panel and wore the number 27 jersey for Cork's All-Ireland semi-final defeat by Limerick on 29 July.[19]
On 16 February 2019, Cadogan played his first game for Cork in eleven months when he came on as a 58th-minute substitute for Jamie Coughlan in Cork's 1-20 to 0-20 National League defeat of Clare.[20] He ended the year by receiving a third All-Star nomination.[21]
On 3 October 2023, Cadogan announced his retirement from inter-county hurling.[22]
On 16 February 2019, Cadogan was part of the coaching team when St. Francis College qualified for the final of the Tom Collum Cup. A 1-13 to 0-14 of Hamilton High School secured the title.[24]