1. Preparing the Crust

1. In a medium bowl, combine graham cracker crumbs, sugar, and melted butter.
2. Press the mixture into the bottom of a springform pan, creating an even layer.
3. Chill the crust in the refrigerator for at least 20 minutes to set.

2. Making the Cheesecake Batter

1. Preheat the oven to 325°F (160°C).
2. In a large bowl, beat the cream cheese and sugar until smooth.
3. Add the sour cream, vanilla extract, and eggs one at a time, beating after each addition.
4. Mix in the cream soda to infuse the batter with Butterbeer flavor.
5. Pour the batter into the prepared crust and smooth the top.

3. Creating the Blackberry Swirl

1. In a saucepan, cook blackberries, sugar, and cornstarch slurry over medium heat until the blackberries break down and the mixture thickens.
2. Let the blackberry sauce cool to room temperature, then swirl it into the cheesecake batter using a knife or toothpick.

4. Baking the Cheesecake

1. Bake for 50-60 minutes, or until the edges are set and the center is slightly jiggly.
2. Let the cheesecake cool completely in the oven with the door slightly ajar, then refrigerate for at least 4 hours before serving.