Preheat oven to 350 degrees F. Grease and flour a bundt pan.
Combine cake mix, vanilla pudding mix, melted butter, vanilla, and milk using an electric mixer. Add eggs one at a time, beating between each addition. Continue to beat for an additional 7 minutes; the batter should be relatively fluffy.
In a separate bowl, combine sugar and cinnamon.
Pour half of cake batter into bundt pan. Evenly cover with cinnamon sugar mixture before covering with the remaining cake batter.
Bake for 45 - 60 minutes; the cake is done when a skewer placed in the depths of the cake comes out clean.
Allow to cool in pan for 10 minutes before carefully removing from pan to cool completely.
While the cake is cooling, prepare icing by whisking together powdered sugar and orange juice. Ice cake once it has cooled completely.