|Batting style||Right-hand bat|
|Bowling style||Legbreak googly|
A lower-order right-handed batsman and a leg-break and googly bowler, Burke, variously known as Cec or Ces, made his first-class debut for Auckland in 1937-38 and then played regularly for the team up to the 1953-54 season. He was picked as a specialist bowler for the single Test match played in 1945-46 between New Zealand and Australia, which was won comprehensively by the Australians, New Zealand failing to total 100 runs in their two innings combined. Burke took two Australian wickets – Bill Brown and Keith Miller.
He was 12th man for the single Test match of the following season, 1946–47, when MCC toured Australia and New Zealand, and was selected for the tour to England in 1949. He had a fairly undistinguished tour, taking 54 wickets at an average of 29.83 and scoring just 171 runs, and did not play in any of the Tests.