Start by preheating your oven to 350°F (175°C). This step is crucial for ensuring your cake rises perfectly.
Grease your bundt pan with cooking spray or butter and flour to prevent sticking.
In a large mixing bowl, combine the cake mix, sour cream, oil, eggs, lemon peel, lime peel, and lemon juice. Use a whisk to mix until well combined and smooth. Avoid overmixing.
Carefully pour the batter into the prepared bundt pan, making sure it's evenly distributed. Tap on the counter to remove air bubbles.
Place the bundt pan in the preheated oven and bake for about 30-35 minutes, or until a toothpick inserted into the center comes out clean.
Once baked, remove the cake from the oven and let it cool in the pan for 10-15 minutes. Then, invert it onto a cooling rack to cool completely.
While the cake is cooling, prepare the frosting. In a bowl, combine the Pillsbury Creamy Supreme Vanilla Frosting with the lemon juice and lime juice. Mix until smooth. Once cooled, drizzle the frosting over the top.