Preheat oven to 350°F (175°C) and grease and flour two 8-inch round pans or one 9x13-inch pan
In a large bowl, mix cake mix, eggs, oil, orange juice, orange zest, and vanilla until smooth
Pour batter evenly into prepared pan(s)
Bake 25–30 minutes for round pans or 30–35 minutes for a 9x13-inch pan, until a toothpick comes out clean
Heat orange juice and sugar in a saucepan until sugar dissolves, then cool slightly
Poke holes in warm cake and spoon syrup evenly over the surface
Cool cake completely
Beat cream cheese and butter until smooth
Gradually add powdered sugar, then mix in cream, orange zest, and vanilla
Frost cooled cake evenly and chill briefly before serving