Congratulations, you are the 12,613th person to ask this very question, and, after ignoring the first 12,612, we are going to answer you. And, we are sad to say, we are going to break many hearts in doing so.
What you want is a theoretical mixture of the primary colors – blue, red, and yellow – that reflects so little light that we perceive it as black. This is the theory in one common printing process, where the three primary colors – cyan, magenta, and yellow – are mixed to produce all the colors needed. In theory, mixing all three colors in sufficient density should produce black. In practice, they produce a muddy brown, so printers generally use a fourth pigment, black, giving us the well-known CMYK printing process, instead of just CMY.
Guess what? The same problem confronts us as cooks. We have never been able to generate a respectable black, certainly not from the little bottles of primary colors available at the grocery store, and also not from creative combinations of multiple paste colors. We can come up with a pretty ugly gray, but we have never achieved black.
There is a reason Wilton, Ateco, AmeriColor, and Chefmaster sell black food color.
We have even more bad news. None of them produce a really black black. There are only so many approved food colors and the commercial manufacturers use a combination of blues, reds, and yellows to create their blacks. Most wind up with at least a hint of purple.
We recently mixed up a batch of buttercream icing and used Wilton’s black paste icing color. Our icing gave the impression of black. The more color we added, the darker it got. But frankly, by the time it was very dark, we didn’t want to eat it, as it turned our mouths and tongues dark, dark, dark purple/black, and we began to imagine what the rest of our insides would shortly look like.
The commercial products do a better job of producing “black” than we have ever accomplished mixing food colors together, but even with their help, you should probably lower your cake and cookie decorating standards.