c. 1610, "younger son or brother;" 1650s, "gentleman entering the military as a profession;" from French cadet "military student officer," noun use of adjective, "younger" (15c.), from Gascon capdet "captain, chief, youth of a noble family," from Medieval Latin capitellum, "little chief," literally "little head" (hence, "inferior head of a family"), diminutive of Latin caput "head" (from PIE root *kaput- "head").
"The eldest son being regarded as the first head of the family, the second son the cadet, or little head" [Kitchin]. Younger sons from noble families were sent to French court to serve as officers, without rising through the ranks or attending military school, after being attached to a corps without pay and enjoying certain privileges. This gave the word its military meaning "accepted candidate for a commission who is undergoing training to become an officer." Meaning "student at a military college" is from 1775.
Via the Scottish form cadee comes caddie "a messenger boy," especially one who carries clubs for a golfer, and slang cad.