Preheat the oven to 350 degrees F. Butter and flour a 9-by-13-inch metal baking pan. Line the bottom of the pan with parchment paper.
Put the flour, baking powder, baking soda and salt in a large bowl and whisk to combine. Put the butter and both sugars in a second large bowl and beat with an electric mixer on medium-high speed until pale and fluffy, about 3 minutes. Add the eggs one at a time, beating well after each addition; beat until smooth, then add the sour cream. Add the flour mixture in 3 additions, alternating with the buttermilk, beginning and ending with the flour. Scrape down the sides and bottom of the bowl with a rubber spatula to ensure the batter is well mixed. Add the grenadine, lemon zest, lime zest and orange zest, and stir until just combined.
Pour the batter into the prepared pan and smooth the top. Bake until the cake is light golden on top and a toothpick inserted into the middle comes out clean, 25 to 30 minutes. Transfer the cake to a cooling rack and let cool for 10 minutes. Invert the cake onto the rack, unmold from the pan and remove the parchment paper. Turn the cake right-side up on the rack and let cool completely before serving.
This recipe was created by a contestant during a cooking competition. It has not been tested for home use.