Preheat oven to 180°C (350°F), with a rack set in the middle of the oven. Lightly grease and flour three 17.5-cm | 7-inch round cake pans, set aside.
Sift flour, cocoa powder, baking powder, baking soda and salt in a medium mixing bowl. Stir to combine, set aside. In another large bowl, or bowl of your stand mixer, beat oil and sugar on medium speed for 2 minutes, until the mixture looks like wet sand. Beat in vanilla and eggs one at a time. Stop and scrape down the sides with a spatula. With speed on low, beat in flour and milk in 3 batches, starting and ending with the flour mixture (flour - milk - F - M - F). Scrape down the sides again. With the mixer on low-medium, slowly pour in the coffee and beat to combine, but no more than 30 seconds.
Evenly divide the batter between the three pans. Bake for 20-25 minutes or until a toothpick inserted into the center of each cake comes out clean. Let cakes cool on a wire rack for 10-15 minutes, then remove them from the pans and let cool completely.
As the cakes bake, make the rum syrup: Combine sugar and water in a small saucepan and cook over medium heat for about 5 minutes or until the sugar completely dissolves. Add rum and bring mixture to a boil. Cook for about a minute, then remove from heat and let cool completely.