Preheat oven to 350 degrees. Grease and flour three 9-inch round cake pans.
In a large mixing bowl, mix the first six ingredients well. Add the eggs, oil, orange juice, lemon juice and vanilla.
Divide the batter evenly among the three pans and bake for 35 to 40 minutes. Test for doneness by lightly touching the tops of the layers or inserting a toothpick. Cool the layers in the pans for 5 minutes, then turn them out onto cooling racks to cool completely.