Preheat your oven to 325°F (160°C). In a mixing bowl, combine graham cracker crumbs, granulated sugar, and melted unsalted butter until the mixture resembles wet sand. Firmly press this mixture into the bottom of a springform pan to form an even crust. Bake for 8-10 minutes until lightly golden, then set aside to cool completely while you prepare the filling.

In a large mixing bowl, beat softened cream cheese and granulated sugar using an electric mixer until smooth and creamy, about 3-5 minutes. Add sour cream and vanilla extract, mixing until well blended. Incorporate eggs one at a time, mixing gently to avoid air pockets, followed by the cream soda.

In a saucepan over medium heat, mix heavy cream, brown sugar, and butter. Stir until the mixture comes to a gentle boil, then reduce the heat and simmer for about 5 minutes until slightly thickened. Remove from heat and divide into smaller bowls, adding food coloring to each.

Pour the creamy cheesecake batter directly onto the cooled crust. Drizzle the colored butterbeer mixtures on top and gently swirl with a toothpick. Bake for 50-60 minutes, or until the edges are set.

After baking, turn off the oven and leave the cheesecake inside with the door slightly ajar to cool gradually for about an hour. Transfer to the refrigerator and chill for at least 4 hours or overnight before serving.