Preheat the oven to 325 degrees, and prep your round bundt pan with a swipe of shortening and dust of flour. Set aside.
In a large bowl, whisk together all the ingredients for the cake except for the cake mix and food gel colors. Sift in the cake mix and gently stir until it's barely combined.
In the 6 separate small bowls, scoop in a generous 1/2 cup of white batter in each bowl. Add one drop(ish) of gel coloring in each bowl, and gently stir to disperse the color throughout. Fill 6 piping bags carefully with the colored cake batter (I love to use a drinking glass to fold the piping bags over for filling the piping bags).
In the bottom of the circle bundt cake, spread in a small layer of the white cake batter (see video for a better visual). Snip off the tip to create a small circle opening (about the size a small marble could get through.
Next, pipe the first color in a ring, avoiding the outside of the first white layer. (I did purple, which technically makes the rainbow upside down - oops! But you can pipe red first for a more traditional look). Tap the pan to make the batter flat before adding the next color.
Next, pipe the second color in a ring around the center of that color stripe (see video). Repeat with the remaining colors - remember to tap the pan to keep it flat before adding in the next color.
Next, add about 1/2 cup of white cake batter into another piping bag. Pipe a white layer in the middle again (just like the previous layers), and tap the pan to flatten.
Finally, pipe the rest of the white cake batter around the top in an even layer. Bake for 25-27 minutes until the center of the cake is baked through. Remove the bundt cake from the oven, let cool in the pan for about 30 seconds, then flip the bundt cake onto a wire rack to cool completely.