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)?

It seems like you're interested in exploring cocktails that harness the refreshing qualities of cucumber alongside the sweet and complex notes offered by sugar-based syrups, rums, and fruity liqueurs. However, from the list of cocktails available, none directly include all the specific ingredients you've mentioned in one singular cocktail. However, we do have a variety of options that focus on cucumber and could be adapted or inspire a concoction of your own.

The Eastern Standard and the Cucumber Lemonade Chiller both use fresh cucumber as a key ingredient, creating a refreshing base that can be further tailored. The Eastern Standard's blend of cucumber, mint, and dry gin along with lime juice and sugar syrup offers a bright and invigorating flavor profile that might align well with your interest in sugar cane syrup. This cocktail, with its relatively high rating of 4.5/5, embodies garden-fresh zest and would serve as an excellent canvas for experimenting with additional ingredients like agave syrup or bitters.

While none of the cocktails listed mention a combination of liqueurs such as cherry or black raspberry, they open the door for creativity. You might consider expanding on them with fruit liqueur undertones, taking inspiration from personal favorites or seasonally available produce. Meanwhile, exploring a rum-based option like a Celery Daiquiri could offer a different base with its daring touch of celery, corresponding well with your noted interest in exploring varying rum styles. Since a perfect match with your specific ingredient list isn't available, creativity and personal taste will be your guide for satisfying your specific craving with the cocktails at hand.