Preheat oven to 350 degrees. Spray three 9-by-2-inch round cake pans with cooking spray, and line with wax paper. Set aside. In a medium bowl, sift together flour and baking soda. Set aside.
In a medium bowl, combine sugar, vegetable oil, eggs, vinegar, and vanilla. With an electric mixer, beat until light and fluffy, about 2 minutes. Gradually add flour mixture, and mix on low speed just until flour has been incorporated. Slowly add buttermilk. Add food coloring, and beat to combine.
Divide batter among pans; each pan will be about half full. Tap pans on counter to remove bubbles. Bake until a cake tester inserted into the middle comes out clean, about 30 minutes. Remove the pans to a rack to cool for 5 minutes. Invert pans onto wire racks sprayed with vegetable oil to cool cake completely, or quick-chill in the freezer for 10 to 15 minutes.
To assemble, place one layer, top side down, on a cake stand. Using an offset spatula, spread with 1/4 inch of frosting. Repeat with remaining layers. To frost the top and sides of the cake, work from the center toward and over the edge, making sure to evenly coat. Store in an airtight container for up to one week.
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