Preheat the oven to 350 degrees F (175 degrees C) and grease/flour a 13 x 9 inch pan.
In a mixing bowl, combine the white cake mix, eggs, vegetable oil, lemon-lime soda, and one package of pistachio pudding mix.
Pour the batter into the prepared pan and bake for 30 to 40 minutes or until a toothpick inserted into the center comes out clean.
Allow the cake to cool completely in the pan.
While the cake is cooling, prepare the frosting by mixing the second package of pistachio pudding mix, whipped topping, and cold milk until well combined and smooth.
Chill the frosting mixture.
Once the cake is cooled, ice it with the chilled pistachio frosting.
Slice and serve the pistachio pudding cake.