First, make the simple syrup. Combine the sugar and water in a saucepan over high heat. Bring to a boil, stirring occasionally, until the sugar has completely dissolved and the liquid has thickened slightly. Simmer for 5 minutes and then remove from heat. Let cool.
Next, add the strawberries, 1/4 cup simple syrup, and 2 tablespoons Rumchata to a food processor or blender. Pulse until smooth.
Distribute the strawberry mixture evenly amongst the 10 paper cups. Place in the freezer for at least one hour.
Rinse the food processor and combine the blueberries, simple syrup, and Bailey’s. Pulse until smooth. Place in the refrigerator until ready to use.
In a large bowl, cream together the cream cheese, sweetened condensed milk, and Rumchata. Scoop or pour into the chilled paper cups on top of the frozen strawberry mixture. The cups should be 2/3 of the way full after adding in the cheesecake layer.
Freeze the cups for 30 minutes, and then press a wooden craft stick into the center of each cup.
Freeze for at least an additional 30 minutes.
Pour in the blueberry mixture and freeze for 30 minutes. Then, sprinkle the graham cracker crumbs on top of each popsicle and freeze again, for at least 6 hours or overnight.
When ready to eat, peel away the paper cup and enjoy!