Sift flour, sugar, baking powder, and salt together into a large bowl.
Make a well in the dry ingredients; place water, oil, egg yolks, vanilla extract, and maple extract into the well. Stir together with a wooden spoon, then beat until batter is smooth; stir in walnuts.
Place egg whites in a large glass or metal bowl. Sprinkle egg whites with cream of tartar; beat until stiff peaks form. Lift your beater or whisk straight up: the egg whites will form sharp peaks.
Use a rubber spatula or wire whisk to fold 1/4 the beaten egg whites into the batter. Gently run the spatula through the center of the bowl, then around the sides of the bowl, repeating until fully incorporated; repeat folding with remaining egg whites, 1/4 at a time, folding just until incorporated. Turn the batter into an ungreased 9- or 10-inch tube pan. Cut through the batter with a knife to eliminate large air bubbles.
Bake in the preheated oven until cake is golden, and a toothpick inserted into the center comes out clean, about 1 hour. Tip the pan upside down over a wire rack to cool, about 30 minutes. Run a knife around the edge of pan to remove the cake; cool completely, about 30 minutes.
Beat instant pudding and milk together in a bowl; fold in whipped cream. Spread over cake.