Preparation
Heat the oven to 350°F. Butter and flour a 10-inch tube pan or 12-cup bundt pan.
To make the cake
Sift the flour, sugar, baking powder, and soda into the large bowl of a stand mixer fitted with the paddle attachment. Add the butter and mix on low speed until fine crumbs form. Change to the whisk attachment. With the machine running on medium speed, whisk in the oil, lemon zest, vanilla extract, and orange juice. Whisk in the eggs one at a time and then increase the speed to high and whisk the batter until light, about 3 minutes, scraping the sides of the bowl if necessary. Pour the batter into the prepared pan and bake until a toothpick inserted in the cake comes out clean, 45 to 50 minutes.
To make the syrup and glaze
While the cake bakes, whisk together in a small bowl the orange juice concentrate, butter, rum, and 1/2 cup of the confectioners’ sugar. When the cake is done, set the pan on a rack to cool for 5 minutes. With a thin skewer, poke the cake all the way through to the bottom of the pan in about 100 places. Pour 1/3 cup of the syrup over the cake and let stand for 1 hour before removing the cake from the pan. (At this point you can wrap the cake in plastic and hold for up to 3 days at room temperature; in fact, the flavor only improves.) Cover the remaining syrup with plastic and store at room temperature.
When ready to serve, whisk the remaining 1/2 cup confectioners’ sugar into the remaining syrup. Set the cake on a rack over a baking sheet and pour the glaze over the cake. Let stand for at least 10 minutes before slicing and serving.
