Step 1

Mix first 6 ingredients in large saucepan. Add 1/2 cup rum; bring to simmer over medium heat, stirring often. Remove from heat. Mix in grated orange and lemon peels, syrup, and baking soda. Let stand until fruit mixture absorbs liquid, stirring often, about 1 hour.

Step 2

Preheat oven to 325°F. Butter 10-inch-diameter springform pan, then line bottom and sides of pan with parchment; butter parchment. Sift both flours and salt into medium bowl. Beat butter and sugar in large bowl until well blended. Beat in eggs 1 at a time. Add flour mixture; beat until just blended. Stir in fruit mixture. Transfer batter to pan. Cover pan with foil.

Step 3

Bake cake 2 hours. Reduce oven temperature to 275°F; continue to bake covered until tester inserted into center comes out clean but slightly moist, about 30 minutes longer. Transfer to rack; remove foil. Pierce top of cake all over with skewer. Drizzle 6 tablespoons rum very gradually over cake. Cool completely in pan. Cut around pan sides to loosen; remove pan sides. DO AHEAD Can be made 3 weeks ahead. Wrap in foil; chill. Bring to room temperature before serving.