Preheat oven to 350 degrees F (175 degrees C).
Grease and flour a 10-inch fluted tube pan (such as a Bundt®).
Beat lemon cake mix, lemon pudding mix, white sugar, eggs, 1 cup peach nectar, and vegetable oil in a bowl with electric mixer on medium speed for 2 minutes.
Pour batter into prepared cake pan.
Bake in preheated oven until top of cake springs back when lightly pressed and a toothpick inserted into the middle of the cake comes out clean, about 50 minutes.
Cool cake in the pan for 15 minutes before removing cake to finish cooling on rack.
Mix confectioners' sugar, 1/4 cup peach nectar, lemon juice, and lemon peel in a bowl to make a smooth frosting.
Place cake on a serving platter; poke holes in top of the cake with a fork. Pour frosting slowly over the cake, allowing frosting to soak into the holes and drizzle down the sides of the cake.