From Caucasus(“mountain range in Eastern Europe between the Black Sea and the Caspian Sea”) + -ian(suffix forming adjectives with the sense ‘from, related to, or like’, or forming nouns with the sense ‘one from, belonging to, relating to, or like’). The anthropological sense (no longer regarded as scientific) was popularized by the German anthropologist and physician Johann Friedrich Blumenbach (1752–1840), based on the belief that the first humans originated from there.
Noun sense 2 (“cocktail”) was popularized by the film The Big Lebowski (1998): see the quotation.
^ Io. Frid. Blumenbach [i.e., Johann Friedrich Blumenbach] (1795), “Sectio IV. Generis humani varietates quinae principes, species vero unica.”, in De generis hvmani varietate nativa[…] [The Natural Variety of the Human Race] (in Latin), 3rd edition, Göttingen, Lower Saxony: Vandenhoek et Rvprecht, OCLC62621989, § 82 (Characteres et limites harum varietatum), page 289.
Johann Friedrich Blumenbach (1752–1840), the German anatomist and naturalist who established the most influential of all racial classifications, invented this name [Caucasian] in 1795, in the third edition of his seminal work, De Generis Humani Varietate Nativa (On the Natural Variety of Mankind). Blumenbach’s definition cites two reasons for his choice—the maximal beauty of the people from this small region, and the probability that humans were first created in this area.