Preheat the oven to 325°F. Line a 9x13-inch baking dish with parchment paper, leaving some overhang for easy removal.

In a medium bowl, combine graham cracker crumbs, melted butter, and 1/4 cup sugar. Mix until well combined. Press the mixture firmly into the bottom of the prepared baking dish to form the crust.

In a large mixing bowl, beat the softened cream cheese until smooth. Gradually add 1 cup of sugar and vanilla extract, mixing until well combined.

Add the eggs one at a time, mixing well after each addition. Stir in the sour cream and heavy cream until smooth.

Divide the cheesecake batter evenly into six bowls. Add a few drops of food coloring to each bowl, mixing until you achieve the desired colors: red, orange, yellow, green, blue, and purple.

Starting with the purple batter, pour a layer into the center of the crust. Follow with the blue batter, allowing it to spread slightly. Continue layering in this order: green, yellow, orange, and finally red. Use a toothpick or knife to gently swirl the colors together for a marbled effect.

Bake in the preheated oven for 45-50 minutes, or until the edges are set and the center is slightly jiggly.

Turn off the oven and leave the cheesecake bars inside for an additional 30 minutes.

Remove from the oven and let cool to room temperature. Refrigerate for at least 4 hours, or overnight, before slicing into bars.