"male child in relation to either or both parents," Old English sunu "son, male child," also broadly "male descendant;" also "second person of the Trinity," from Proto-Germanic *sunus (source also of Old Saxon and Old Frisian sunu, Old Norse sonr, Danish søn, Swedish son, Middle Dutch sone, Dutch zoon, Old High German sunu, German Sohn, Gothic sunus "son").
The Germanic words are from PIE *su(H)nus "son" (source also of Sanskrit sunus, Greek huios, Avestan hunush, Armenian ustr, Lithuanian sūnus, Old Church Slavonic synu, Russian and Polish syn "son"), a derived noun from root *su(H)- "to give birth" (source also of Sanskrit sauti "gives birth," Old Irish suth "birth, offspring").
The sense of "person whose character partakes so much of some quality as to suggest the relation of a son to a parent" was in Old English. As "person regarded as the product of some place," 1590s.
Son of _____ as the title of a sequel to a book or movie is recorded from 1917 ("Son of Tarzan"). Most explanations for son of a gun (1708) are more than a century after its appearance. Henley (1903) describes it as meaning originally "a soldier's bastard;" Smyth's "Sailor's Word-Book" (1867) describes it as "An epithet conveying contempt in a slight degree, and originally applied to boys born afloat, when women were permitted to accompany their husbands to sea ...."