Preheat the oven to 350°F (175°C). Spray a 12-cup bundt pan with nonstick spray and set aside.
In a medium bowl, whisk together the 3 cups all-purpose flour, 2 teaspoons baking powder, 1 teaspoon salt, and 1/2 teaspoon baking soda. Set aside.
In a large bowl, use a hand mixer on medium speed to beat 2 1/4 cups granulated sugar, 1 cup (2 sticks) unsalted butter (room temperature), and 1/4 cup vegetable oil for 4 minutes, until the mixture is light and fluffy.
Beat in the 4 large eggs one at a time, mixing until each egg is incorporated before adding the next. Add 1 tablespoon vanilla extract and beat for 2 more minutes.
Reduce the mixer speed to low. Alternately add the flour mixture and 1 1/3 cups buttermilk to the butter mixture, making three additions of the flour mixture and two additions of the buttermilk, beginning and ending with the flour mixture. Beat only until each addition is incorporated; do not overmix.
Divide the batter equally among six small bowls (about 1 1/3 cups per bowl). You may leave one portion in the mixing bowl.
Color each portion: stir red food coloring into one bowl, orange into the next, then yellow, green, blue, and purple. If using liquid food coloring start with about 4 to 8 drops per bowl; if using gel or paste, use a small amount of gel. Stir each bowl until the color is even.
Transfer the batters to the prepared bundt pan in this order: red, then orange, then yellow, then green, then blue, then purple. Spoon each color into the pan and spread lightly with a spoon or offset spatula to make even layers. Try not to swirl the colors together.
Gently tap the pan once or twice on the counter to help level the layers and release any large air pockets.
Bake for 55 to 65 minutes, until the cake is puffed, golden brown, and a tester inserted into the center comes out clean.
Let the cake cool in the pan on a wire rack for 10 minutes. Carefully invert the cake onto the wire rack and let it cool completely.
To make the glaze, in a medium bowl whisk together 3 cups powdered sugar, 1 teaspoon finely grated lemon zest, and 4 tablespoons freshly squeezed lemon juice until smooth. If the glaze is too thick, whisk in additional lemon juice 1 teaspoon at a time (up to a total of 5 tablespoons) until the glaze is thick but pourable.
Pour the glaze over the cooled cake, allowing it to drip down the sides. Let the glaze set for at least 15 minutes before serving.