Grease 3 (8-inch) round cakepans. Line with wax paper; grease and flour.
Combine cake mix and streusel packet in a mixing bowl, reserving glaze packet. Add eggs, 1 1/4 cups water, and oil; beat at medium speed with an electric mixer 2 minutes. Stir in carrot, pecans, and coconut. Pour batter evenly into prepared pans.
Bake at 350° for 18 to 20 minutes. Cool in pans on wire racks 10 minutes. Remove from pans; place on racks.
Stir together reserved glaze and juice; brush evenly over warm cake layers. Cool completely on wire racks.
Spread Cream Cheese Frosting between layers and on top and sides of cake. Chill at least 2 hours.