Preheat oven to 350º F. Prepare three 9-inch cake pans by spraying with baking spray or buttering and lightly flouring.
Whisk together the flour, sugar, baking soda, baking powder, salt, and ground cinnamon in a large bowl. Set aside.
Cream together the eggs, oil, vanilla extract, pineapple, mashed bananas, and finely chopped pecans in another large bowl. Stir the egg mixture into the flour mixture until just combined. Evenly divide the batter between the three prepared pans and bake for about 20 to 25 minutes, or until a toothpick or skewer inserted in the center of the cake comes out clean.
Remove from the oven and allow to cool for about 10 minutes. Turn cakes onto a wire rack and allow to cool completely before frosting with cream cheese frosting.