Preheat your oven to 325°F (160°C). In a medium bowl, combine graham cracker crumbs, granulated sugar, and melted unsalted butter. Mix until you achieve a crumbly texture. Press the mixture firmly into the bottom of a 9-inch springform pan. Bake for 8-10 minutes or until golden and fragrant. Once done, allow the crust to cool completely before adding the cheesecake mixture.

In a large mixing bowl, beat the cream cheese with granulated sugar using an electric mixer until creamy and smooth. Gradually add in the sour cream and vanilla extract, mixing until fully incorporated. Next, add eggs one at a time, ensuring each is blended in well. Finally, pour in the cream soda and blend until the batter is uniform, making sure there are no lumps.

In a small saucepan over low heat, gently heat the heavy cream, brown sugar, and butter until the mixture begins to boil. Allow it to simmer for about 3-4 minutes, stirring frequently. Remove from heat, and stir in the vanilla extract. Divide the mixture into four separate bowls and use gel food coloring to tint each one a different house color: red, yellow, blue, and green.

Pour the smooth cheesecake batter over your cooled crust, creating an even layer. Drizzle the colored mixtures on top of the batter, creating a beautiful marbled effect. Use a toothpick or a knife to gently swirl the colors together, being careful not to overmix. Bake in the preheated oven for about 50-60 minutes until the edges are set but the center has a slight jiggle.

After baking, turn off the oven and crack the door open, allowing the cheesecake to cool gradually for about an hour. Once it’s cooled, transfer the cheesecake to the refrigerator and chill for at least 4 hours, or preferably overnight. Before serving, consider decorating the top with additional swirls of the colored cream and a sprinkle of gold dust.