Preheat the oven to 475 degrees F. Place a pan of warm water on the lowest shelf in the oven.
In a mixing bowl, beat the cream cheese until light and fluffy, scraping the sides and bottom of the bowl a few times to dislodge any unbeaten cream cheese.
Mix in the sugar and flour and beat until smooth.
Add the lemon and orange zest and the vanilla. Stir just until mixed.
Add the eggs, one at a time, beating after each addition until thoroughly mixed.
Stir in the heavy cream and mix until just blended. Do not overbeat.
Divide the batter equally between the seven bowls. To the first bowl, add the red gel coloring. To get a deep, rich red color, add approximately 1/2 to 1 teaspoon. Red usually takes the most color to make a vibrant red color. Stir well to blend.
To the second bowl, add orange gel coloring. Add enough orange gel to achieve the same depth of color as the red batter. Stir until well blended. Add additional coloring as needed.
In the third bowl, add yellow gel color. Add enough coloring to reach the same depth as the other two colors. Stir to mix.
Add the green gel coloring to the fourth bowl, again matching the color depth as the previous colors. Stir well.
In the fifth bowl, add the blue gel color. This color should be vibrant sky blue. Stir well.
To the sixth bowl add twice the amount of blue added to the fifth bowl. Stir well. This blue color should be twice as dark as the blue in the previous bowl. If not, add a little more blue gel coloring. Now add a small amount of violet gel coloring and a small amount of black gel coloring. Stir. This color should be a dark indigo color.
In the seventh bowl, add violet gel coloring. It should match the depth and vibrancy of the other colors. Stir well.
To assemble the cheesecake, start with the red batter and pour it into the center of the crust. Let it spread on its own.
Next, pour the orange batter directly on top of the red batter. Do not spread out the batter to prevent the blending of colors. Continue adding the batters (yellow, green, blue, indigo, and violet) one on the other without spreading them.
Bake at 475 degrees F for 15 minutes. Then reduce the oven temperature to 200 degrees F and bake for 1 hour. When finished baking, turn off the oven and let the cheesecake sit in it for 2 hours. Do not open the oven door during this time.
Remove the cheesecake and let cool. Refrigerate for several hours. Serve cold.