Lower oven temp to 325 degrees.
Add 1-2 inches of warm water to a roasting pan or large rimmed cookie sheet and place on the bottom oven rack. Allow it to heat up for 5-10 minutes before baking your cheesecake.
In a stand mixer fitted with the paddle attachment or a hand mixer, beat the softened cream cheese until smooth. Scrape down the bowl once complete.
Add sugar, sour cream, vanilla extract, flour and salt. Beat on high until smooth. Scrape down the bowl once complete.
Add in eggs, one at a time, beating on low after each addition until combined. Do not over beat.
Equally separate the batter into four separate bowls.
Add 3-4 drops of different colored dye to each bowl and stir well. Add additional drops if needed to reach desired color. For this cheesecake I used green, yellow, pink and purple dye.
Use a spoon or a cookie dough scoop to alternate adding each color to the pan (see photos above). Once all of the batter has been added, use a butter knife to swirl the batter. Make 5-6 figure-eights in the batter, ensuring that the knife is gliding all the way along the crust (without breaking the crust).
Bake for 60-90 minutes, or until there is a 3 inch jiggle in the center. Then turn off the oven and leave the cheesecake in the oven for another 1-2 hours or until the oven has cooled to room temperature.
Remove the cheesecake from the oven and let it cool completely to room temperature (another 1-2 hours), then place it in the refrigerator overnight to set.
Remove the spring form once the cheesecake has cooled to room temperature or after chilling overnight. Run a butter knife around the edges of the pan to loosen it first.