Combine rum, lemon juice and simple syrup and shake vigorously over ice for 10 seconds. Strain over cucumber ice cubes mixed with clear ice cubes into a highball glass; top with soda and garnish with basil and lemon wheel. Yields 1 cocktail.
*Combine 1 cup granulated sugar and 1 cup water in a saucepot over low heat until sugar dissolves. Cool and pour into a clean bottle. Refrigerate up to 2 weeks.
**Purée 2 peeled and seeded English cucumbers with 2 tablespoons water in a blender and pour into an ice cube tray. Freeze 6 hours or overnight. For the stacked cucumber cube effect, add layers of clear ice cubes between cucumber cubes.