For the buttercream, I piped the inside color directly on the cake and then piped the outlining color and then after the crusted enough I used a paper two to smoosh it together.
On the fondant cake, I just used a paint brush and my airbrush colors and painted on the spots. I like using the airbrush colors because they dry well. You can use color gels or dusts mixed with lemon extract or vodka/everclear as well.
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I have only done it with a paint pallette, and watered down food coloring. Just test the colors first, on paper or something to make sure your colors are light enough. Sometimes it can be a little dark, and hard to see the different shades, that make it so awesome!
I used Wilton coloring watered down a little with clear vanilla extract. Find a good photo of a cheetah print to look at while you are painting and it will give you ideas on how to make them cheetah-like but random, like cheetah spots are supposed to be.
I made a cheetah cake not long ago. I found this cake by sweetcakes and she shows photos as she is piping the buttercream. Then, as TexasSugar said, let it crust a bit and then smooth with viva and a fondant smoother. It could not have been simpler. I don't have an airbrush, so I made my base buttercream the shade of tan that I wanted and even left some streaks in the color so that it would not be totally uniform in color. You can go to my photos and see my cheetah cake. This link is to the cake by sweetcakes. Look at her "other photos" on this cake to see the before viva papertowel photos. Good luck