Special equipment: six 8-inch round cake pans; a pastry bag fitted with a large round tip
Preheat the oven to 375 degrees F. Spray the bottom and sides of six 8-inch round cake pans; dust with flour and tap out excess.
Whisk together the flour, baking powder and salt in a medium bowl; set aside.
Beat the butter, sugar and oil in a large bowl with an electric mixer on medium-high speed until light in color and fluffy, about 5 minutes. Beat in the eggs, one at a time, then the vanilla seeds, until combined.
Transfer the creamed mixture to a very large mixing bowl, then alternate folding in the flour mixture and the milk with a spatula, adding the flour in 3 additions and the milk in 2, starting and ending with the flour, just until smooth. Divide the batter equally among 6 mixing bowls. Using gel food colors, tint each bowl with one of the colors of the rainbow. Pour each color into its own prepared cake pan.
Bake, rotating the pans halfway through, until a toothpick inserted in the centers comes out clean, 18 to 20 minutes. Cool the cakes in the pans on a rack for 10 minutes, then remove the cakes to the rack to cool completely.
Level the tops of any cake layers that have domed by slicing the domes off with a serrated knife. Put some buttercream into a pastry bag fitted with a large round tip. Put the bottom cake layer onto a cake plate. Pipe around the edge of the cake layer to create a frosting "dam." Fill the center with a thin layer of jam (about 1/2 cup). Top with another cake layer and repeat until you have stacked and filled all the layers. Frost the outside of the cake with the remaining buttercream and decorate as desired.
In the bowl of a stand mixer, combine the confectioners' sugar, butter, milk, vanilla seeds and salt. Beat on low speed for a while. When the sugar is incorporated, turn the speed up and beat until the buttercream is fluffy and smooth. If it's too wet, add a bit more confectioners' sugar. If it's too stiff, add a bit more butter. Be sure to scrape the sides of the bowl once or twice to make sure everything is combined.
Use immediately or store in an airtight container at room temperature for up to 24 hours or in the fridge for up to 2 weeks. Rewhip cold buttercream before using.