What cocktails can I make with cucumber (fresh), sugar cane syrup (from juice), sugar cane juice, agave syrup, Angostura or other aromatic bitters, triple sec, passion fruit liqueur, cherry (brandy) liqueur, black raspberry liqueur (e.g. Chambord), and rum (all styles)?

Looking through the list of cocktails in relation to your ingredients, it appears two options could interest you: the "Gin and Cucumber," which features fresh cucumber and sugar syrup, and the "English Cucumber Martini," which utilizes mint leaves similar to the fresh, light flavors of cucumber and sweet touches from lemon syrup. While neither cocktail includes all your ingredients, they both make excellent use of fresh cucumber and a sweetening element, which might inspire some experimentation in crafting a delicious cucumber-based drink.

The Gin and Cucumber cocktail, with its refreshing blend of gin's botanical quality and cucumber's crisp essence, is elevated by the tang of added lemon juice and sugar syrup. The inclusion of tonic water gives it a bubbly effervescence, making it soothing for warm weather or a sophisticated choice for social gatherings. On the other hand, the English Cucumber Martini offers a quaint British charm with its notes of Pimm's No. 1 and the lush touch of Calvados, coupled with mint and lemon syrup, combining to create a delightful garden-inspired experience. Although neither cocktail involves the full array of your ingredients, these choices serve as a fantastic starting point for a cucumber-forward, refreshing cocktail adventure.