Place 5 cucumber slices in a cocktail shaker. To muddle, gently crush cucumber with the back of a spoon. Add rum, lemon juice, and Simple Syrup. Add ice cubes; cover and shake until very cold. Strain liquid into an ice-filled glass. If desired, garnish with additional cucumber slices.
In a small saucepan combine sugar and water. Bring to boiling over medium heat, stirring until sugar is dissolved. (The syrup is done when it is completely clear and the surface is covered with bubbles.) Remove from heat; cool. Store, covered, in the refrigerator up to 2 weeks.