Preheat the oven to 350°F (175°C). Lightly grease a 9x13-inch baking pan with nonstick spray or butter to prevent sticking. Set aside.

In a large mixing bowl, combine the white cake mixes, eggs, water, oil, and tequila. Using an electric hand mixer or a stand mixer fitted with a paddle attachment, mix until the batter is smooth and fully combined. Gently fold in the blackberries using a rubber spatula, being careful not to crush them excessively.

Pour the batter into the prepared baking pan. Bake in the preheated oven for 30 to 35 minutes, or until a toothpick inserted into the center of the cake comes out clean. Remove from the oven and allow the cake to cool in the pan on a wire rack while preparing the glaze.

In a medium saucepan over medium heat, melt the butter together with the milk. Stir continuously and bring to a gentle boil. Once the mixture reaches a boil, remove the saucepan from the heat. Stir in the confectioners’ sugar, lime extract, tequila, and lime zest until a smooth glaze forms.

While the cake is still slightly warm, pour the glaze evenly over the surface, allowing it to soak slightly into the cake. Use an offset spatula or the back of a spoon to distribute it evenly if needed.

If desired, pipe or drizzle the blackberry dessert sauce in horizontal lines across the top of the cake. Using a knife or skewer, drag vertically through the lines to create a marbled effect. Alternatively, simply drizzle the sauce over the top for a more casual finish.

Once the cake is fully cooled and the glaze has set, slice into squares and serve.