Preheat the oven to 325 degrees, and make sure the oven rack is in the middle of the oven.
Place the Graham Crackers in a food processor or blender, and pulse until you have fine crumbs.
Place the Butter in a bowl, and microwave for about 30 seconds, or until the Butter is melted.
Pour the Graham Cracker Crumbs into the bowl of melted butter, and add the Sugar on top of the crumbs.
Stir together until the crumbs are coated in the Butter.
Line the Bottom of a 9 inch Spring-form pan with Parchment Paper, and pour the Crust mixture on top of the Parchment, and press evenly into the bottom of the pan with the back of a large spoon. Set aside.
In the mixing bowl of a stand mixer, add the Cream Cheese, Whipping Cream, Sugar, Vanilla and Eggs, and mix on low until blended.
Turn up the Mixer to medium high, and mix well. Scrape down the sides of bowl and mix again to make sure the batter is smooth.
Add the Flour and Rum, and mix on low until blended into the batter.
Scrape down the sides of the bowl, and turn the mixer speed up to medium high, and blend until well mixed.
Divide the Batter into three equal amounts, using 2 bowls, and pour 1/3 of the Batter into each bowl, and leave 1/3 of the Batter in the mixing bowl.
In one bowl, add the Tablespoon of Cherry Juice, and stir to mix. Add several drops of Pink Food Coloring Gel, and then 2 or 3 drops of Red Food Coloring Gel, and stir well. Stir until the Food Coloring Gel is completely mixed, and you should have the pinkish red layer; if the color is not bright enough, add more pink, and a little more red Food Coloring Gel to the bowl, and stir well, until you get the desired color.
In the other bowl, add the Orange Food Coloring Gel until you get a bright Orange color.
Starting with the Pink Batter, pour the Pink Batter into the Spring-form pan, on top of the Graham Cracker Crust.
Pour the Orange Batter on top of the Pink Batter, pouring in the middle of the pink batter.
Pour the White Batter in the Mixing bowl right in the middle of the Orange Batter - Batter will move around in the pan, and that's okay, it will make the layers and colors very similar to the Malibu Sunset Cocktail, only as a Cheesecake. Carefully place the Spring-form pan in the oven, right in the center of the oven.
Place a small dish of Water right underneath the Cheesecake/pan.
Bake the Cheesecake for about 1 1/2 hours, to 1 hour and 45 minutes, or until the Cheesecake is no longer runny in the center, and only wobbles a little in the center when jiggled.
You'll need to watch the Cheesecake after about an hour, to jiggle the pan just slightly, and when it's ready to take out, the center will only wobble a little, like Jell-O when it's set, or firm.
If the Cheesecake still appears really wiggly in the center, or runny, it's not done.
Continue to bake until the center is a Jell-O like consistency.
When the Cheesecake is done, turn off the oven, and leave the Cheesecake in the Oven for 10 minutes, then remove the pan from the oven to a wire rack, and cool completely.
When Cool, wrap in Parchment Paper, and Aluminum Foil, and place in the Refrigerator overnight.
The next day, make the Butter Cream Frosting:
Place the softened Cream Cheese, and Butter in the mixing bowl of a stand mixer, and mix until completely smooth and creamy.
Add the Whipping Cream, Vanilla, and Salt, and mix until smooth and creamy.
Add the Powdered Sugar 1 cup at a time, blending between additions, until all the Powdered Sugar has been added. Add several drops of bright Yellow Food Coloring Gel to the Frosting, until you have a bright Yellow color.
Using a large Whipped Cream Tip, (SEE LINK) place the tip in a pastry bag, and fill the bag with the Frosting.
Remove the Cheesecake from the refrigerator, and remove the Spring-form from the pan.
Place the pan on a Cake Stand, or Cake Plate, and pipe the Frosting on the top of the Cheesecake, around the edges, and in the center, making big fluffy dollops all around the Cheesecake.
Place Maraschino Cherries on top of the Dollops, and Orange Slices between Dollops of Frosting, so that each piece has the Fruit garnish served.
Place the Cheesecake back in the refrigerator until time to serve.