Only capitalize “cadets” when used as a title (Cadets Sanderson and Salazar) or as part of the phrase “Corps of Cadets,” not as a common noun (The cadets leave for winter furlough after their last exam.).
Capitalize “Corps” when used alone to refer to the entire unit of cadets.
Corps of Cadets
Capitalize both “C’s” (and remember the “s” in “Corps”).