For the cake and orange syrup:
Vegetable oil spray, for misting the pans
Flour, for dusting the pans
1 package (18.25 to 21.6 ounces) yellow cake mix
1 package (3.4 ounces) vanilla instant pudding mix
3 large eggs
½ cup vegetable oil
1 teaspoon pure vanilla extract
1⅓ cups plus ¾ cup orange juice for the syrup
1 tablespoon grated orange zest
2 tablespoons sugar
For the frosting:
8 tablespoons (1 stick) butter, at room temperature
4 ounces cream cheese, at room temperature
1 teaspoon grated orange zest
2 to 3 teaspoons orange juice
3 ¾ cups confectioners’ sugar, sifted
Place a rack in the center of the oven and preheat the oven to 350 degrees. Lightly mist or grease two 9-inch round cake pans and dust them with flour. Set the pans aside.
Place the cake mix, pudding mix, eggs, oil, vanilla, 1⅓ cups of orange juice, and orange zest in a large mixing bowl. Beat with an electric mixer on low speed until incorporated, 30 seconds.
Increase the mixer speed to medium and beat until the mixture lightens and is smooth, 1½ minutes.
Pour the batter into the prepared pans, smoothing the top with a rubber spatula, and place the pans in the oven.
Bake the cake until it is golden brown and the top springs back when lightly pressed with a finger, 28 to 33 minutes.
Meanwhile, make the orange syrup. Pour ¾ cup orange juice into a small bowl and add the 2 tablespoons sugar. Whisk until the sugar dissolves and set aside.
Remove the cake layers from the oven and let them cool in the pans for 10 minutes. Run a knife around the edges, gently shake the layers to loosen the cake, and invert them once, then again, onto wire racks to cool right-side up.
Let cool 20 minutes longer. Poke holes in the top of each layer with a bamboo skewer or chopstick and slowly spoon the orange syrup over the surface. Allow the layers to cool to room temperature, 30 minutes more.
Meanwhile, make the frosting.
Place the butter and cream cheese in a large mixing bowl and beat with an electric mixer on low speed until combined, 30 seconds. Add the orange zest, 2 teaspoons orange juice, and confectioners’ sugar a little at a time, beating with the mixer on low until the sugar is incorporated, 1 minute. Increase the mixer speed to medium and beat until the frosting is fluffy, 1 minute longer.
Add up to 1 teaspoon more orange juice if the frosting seems too stiff.