Preheat oven to 350°F. Brush an 8-inch round cake pan with 2-inch-high sides with butter. Whisk together flour, baking powder, baking soda, and salt in a medium bowl.
In a mixer, beat butter with sugar and zest on medium speed until light and fluffy, 2 to 3 minutes. Add eggs, one at a time, beating well after each addition. Beat in vanilla and sour cream, scraping down sides of bowl. Reduce speed to low and gradually add flour mixture.
Slice the ends off each blood orange and then cut away the peel, following the curve of the fruit to remove the white pith. Slice peeled oranges crosswise into ¼-inch-thick wheels, making sure to remove any seeds. In a small bowl, stir together butter, sugar, and rum, if using. Pour and spread mixture over bottom of prepared cake pan. Arrange sliced citrus over it in a tight, slightly overlapping even layer.
Carefully spread cake batter over citrus (it will be thick). Bake until cake is golden and a tester inserted in the center comes out clean, about 55 minutes. Transfer pan to a wire rack and let cool for 30 minutes. Invert onto a cake plate and serve, warm or room temperature.