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It's called 'Save Room' by John Legend. The complete list of songs can be found here with corresponding scene descriptions and music samples.
The cocktail that Jacob drinks and makes throughout the movie is an "Old Fashioned," considered by some historians to be the first American cocktail. The recipe usually included sugar and bitters muddled together, club soda and ice, rye whisky, and a large slice of orange peel.
The song was "Starlight" by Muse. It does not appear in the actual film.
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