Preheat your oven to 350°F (175°C). Prepare your springform pan by ensuring it is leak-proof. Wrap the outside with foil to prevent water from entering during the water bath.
In a bowl, combine graham cracker crumbs, sugar, and brown sugar. Mix well. Add melted butter and stir with a fork until the crumbs are evenly coated.
Press the mixture firmly into the bottom and slightly up the sides of the pan. Bake for 6 minutes. Remove from the oven and let it cool completely.
In a large bowl or stand mixer, beat the cream cheese until smooth and creamy. Add sugar and mix until well combined.
Add vanilla extract and salt. Mix again. Stop occasionally to scrape down the sides and bottom of the bowl with a spatula.
With the mixer on low speed, slowly add the beaten eggs one at a time. Mix gently until just combined. Do not overmix.
Fold in the sour cream until smooth.
Divide the cheesecake batter evenly into six Ziplock bags or bowls. Add a few drops of food coloring gel to each portion and mix until you reach your desired shade.
Cut the corner of each bag and pipe the colored batter randomly into the crust. Alternate colors to create a layered look.
Use a butter knife to gently swirl the colors. Do not overmix; swirl only a few times for a beautiful marble effect.
Place the springform pan into a roasting pan. Fill the roasting pan halfway with hot water.
Bake for 45–50 minutes, or until the edges are firm but the center still slightly jiggles.
Turn off the oven and leave the cheesecake inside for 1 hour with the door closed.
Remove the cheesecake from the water bath and let it cool on a rack. Refrigerate for at least 4 hours, preferably overnight.
Slice, serve, and enjoy your colorful Superman cheesecake.