Preheat the oven to 350 degrees.
Grease three 8” cake pans with nonstick spray, butter, or cake release, and line with parchment and grease the parchment. Wrap the pans with baking strips, if using. Set aside.
Into the bowl of a stand mixer fitted with the paddle attachment, place the cake mix, pudding mix, and matcha powder. Blend on low for about 30 seconds to combine. You can alternatively use a hand-held mixer.
Add the eggs, sour cream, oil, vanilla, and milk. Combine on medium speed for two minutes, stopping about halfway to scrape the bowl and blade.
Evenly divide the batter between the three pans.
Bake for 25 to 30 minutes, or until a toothpick inserted in the middle of a cake comes out with a few moist crumbs attached. Adjust baking times as needed for your oven.
Remove the cakes from the oven and remove the baking strips, if using. Allow the cakes to cool in their pans for 20 minutes.
Invert the cakes onto a rack to finish cooling. (At this point, you can wrap in double layers of plastic wrap and refrigerate or freeze until ready to use.)