Assemble all necessary ingredients. Preheat your oven to 325 degrees Fahrenheit (165 degrees Celsius). Use a sufficient amount of butter to generously grease a 10-inch fluted tube pan, such as a Bundt pan.

In a large mixing bowl, combine the granulated sugar and softened butter. Using an electric mixer, beat these ingredients until the mixture is light and fluffy.

Introduce the eggs one at a time, ensuring each egg is fully incorporated into the mixture before adding the next. This will help maintain the structure of the batter.

Gradually add the sifted all-purpose flour to the mixture, incorporating one cup at a time. Ensure each addition is well blended to achieve a smooth batter.

Stir in the lemon extract to infuse the batter with flavor. Following this, gently mix in the lemon-lime carbonated beverage until the batter is homogeneous.

Carefully pour the batter into the prepared fluted tube pan, smoothing the top with a spatula.

Place the cake in the preheated oven and bake for approximately 75 minutes, or until a toothpick inserted into the center of the cake comes out clean.

Once baked, immediately remove the cake from the oven and prepare to unmold by placing a wire cooling rack over the base of the cake. Invert the pan to release the cake onto the rack.

While the cake cools slightly, prepare the glaze by beating together the sifted confectioners' sugar, milk, and vanilla extract in a mixing bowl using an electric mixer set to medium speed. Continue mixing until the glaze is smooth and free of lumps.

Drizzle the prepared glaze over the warm cake, ensuring it is evenly covered.

Allow the cake to cool completely, permitting the glaze to set before serving.