Preheat oven to 350 degrees (F).
Combine the cake mix, pistachio pudding mix, orange juice, water, eggs, and oil in a large mixing bowl. Blend to moisten, then beat 2 minutes at medium speed.
Pour about 3/4 of the batter into a well-greased and floured Bundt pan.
Add the chocolate syrup to the remaining batter and mix well.
Pour over the batter in the pan.
Bake for 45 to 60 minutes or until a toothpick inserted in the cake comes out clean.
Cool cake for 10 minutes then invert onto a serving platter. Allow to cool completely.
For the chocolate drizzle, stir the confectioners' sugar, chocolate syrup, and orange juice together until smooth. Drizzle over the completely cooled cake. Allow to set for 15 minutes before adding the orange drizzle.
For the orange drizzle, stir the confectioners' sugar, orange juice, and orange extract together until smooth. Drizzle over the cake. Allow to set 15 minutes before serving.