Unsalted butter, for greasing pan
1 cup flour, plus more for pan
1 cup sugar
2 tbsp. coconut-flavored rum
1 14-oz. can sweetened condensed milk
1 13.5-oz. can coconut milk
1 12-oz. can evaporated milk
Poached peaches in syrup, cut into eighths, to garnish
Heat oven to 350°. Grease and flour a 9″ springform pan; set aside. In the bowl of a stand mixer, beat sugar and eggs on high speed until tripled in volume, pale, and thick, about 12 minutes. Add flour and gently fold with a rubber spatula until just combined; pour batter into prepared pan and smooth top. Bake until golden brown and a toothpick inserted in the middle of the cake comes out clean, about 40 minutes. Let cool.
In a large pitcher, whisk together rum and condensed, coconut, and evaporated milks. Pierce cake all over with a toothpick and slowly drizzle milk mixture over top. Chill until milks are completely absorbed, about 4 hours or overnight. To serve, slice into wedges and top with a poached peach wedge.