Preheat the oven to 350°F (180°C), or 160°C if using a fan oven. Lightly grease an 18x13x1 inch (approx 45x33x2.5 cm) sheet tray with baking spray and set aside.
In a medium bowl, stir together the flour, baking soda, and salt.
In a large bowl, whisk together the sugar, 7Up, oil, sour cream, eggs, lemon zest, lime zest, and vanilla until smooth.
Add the flour mixture to the 7Up mixture and whisk to combine until smooth with no lumps.
Add the 7Up cake batter to the prepared sheet tray and smooth it out into an even layer.
Bake for 20-23 minutes or until a toothpick inserted into the center of the cake comes out clean.
Just before the cake is done baking, begin to make the frosting. Add the butter and 7Up to a medium-sized sauce pot over medium heat.
Stir constantly until the mixture comes to a boil. Remove from the heat and whisk in the powdered sugar a little at a time until you have a smooth, pourable icing.
Add the lemon zest, lime zest, and vanilla, and stir to combine.
Immediately pour the lemon lime frosting over the warm cake and use an offset spatula to smooth it over the entire cake.
Allow to cool completely and serve.