Preheat oven to 325F. Grease and flour a 12-cup bundt pan.
In a medium bowl, whisk together flour, baking soda, baking power and salt.
In a large bowl, cream together butter and sugar until light. Beat in the eggs one at a time, followed by the vanilla extract. Working in two or three additions, alternate adding the flour mixture and the milk large bowl, ending with an addition of flour, and mixing just until everything is incorporated.
Remove 1 cup of the batter into a small bowl. Remove another cup of batter into a second small bowl. * Add espresso to one of the small bowls and whisk until well-combined. Add Kahlua to the second small bowl and whisk until well combined.
Pour half of the plain batter into the bundt pan and spread into an even layer. Pour the Kahlua batter into an even layer on top of the plain batter. Pour espresso batter on top of Kahlua batter. These batters may be slightly thinner, but do not mix or stir them. Carefully spread all remaining plan batter into the bundt pan.
Bake for 55-60 minutes, until a toothpick inserted into the center comes out clean.
Let cake cool in pan for 15-20 minutes, then turn cake out onto a wire rack to cool completely before frosting.