Preheat your oven to 325°F (160°C). In a mixing bowl, combine graham cracker crumbs, granulated sugar, and melted butter until the mixture resembles wet sand. Firmly press this crumb mixture into the bottom of a 9-inch springform pan. Bake for 8–10 minutes until lightly golden and set. Remove from the oven and allow it to cool completely before adding the cheesecake filling.

In a large mixing bowl, beat the softened cream cheese and granulated sugar together with an electric mixer until smooth and creamy. Gradually mix in the sour cream and vanilla extract until well combined. Add the eggs, one at a time, mixing gently after each addition to keep the batter smooth. Finally, pour in the cream soda and mix until fully incorporated.

In a medium saucepan, bring the heavy cream, brown sugar, and butter to a gentle boil over medium heat. Stir continuously until the sugar has dissolved and the mixture is smooth. Remove from heat, then stir in the vanilla extract. Divide this mixture into several small bowls, adding different gel food colorings to each.

Pour the cheesecake batter over the cooled graham cracker crust in the springform pan. Carefully spoon the colorful butterbeer mixtures over the cheesecake batter, allowing them to float on top. Using a knife or a skewer, gently swirl the colored mixtures into the batter for a marbled effect. Bake in the preheated oven for 50–60 minutes.

After baking, turn off the oven and let the cheesecake cool in the oven with the door slightly open for about an hour. Once cooled, transfer the cheesecake to the refrigerator and chill for at least 4 hours or overnight for best results.