Lightly grease the bottom and about 2 inches up the sides of a 5- to 6-quart slow cooker with nonstick spray or a thin smear of oil, and add a parchment strip with overhanging handles if desired.

In a large bowl, whisk together the white cake mix and instant key lime or lime pudding mix until the pudding powder is evenly distributed.

Pour in 1 cup of key lime or lemon-lime soda and the 1/3 cup oil, then stir with a spoon or spatula just until the batter is smooth and combined.

Scrape the batter into the prepared slow cooker and smooth the top into an even layer.

Cover and cook on HIGH for 2 to 2 1/2 hours, or on LOW for 3 1/2 to 4 hours, checking toward the earlier end of the range; the cake is done when the center is set, the top looks dry, the edges pull back slightly, and a toothpick comes out with a few moist crumbs but no wet batter.

Turn off the slow cooker, carefully remove the lid, and let the cake cool in the insert for at least 20 to 30 minutes.

While the cake cools, whisk the powdered sugar with 2 tablespoons of soda until smooth, adding up to 1 more tablespoon of soda a little at a time if needed to make a thick but pourable glaze.

Drizzle the glaze over the warm cake, let some soak into the top, then slice into squares or wedges and serve warm or at room temperature.