Add the first listed 6 ingredients in a large pan.
Then pour in 1/2 cup of rum and let it simmer on a medium flame. Stir it continously, then remove it from the stove.
Next, add in the grated orange and lemon peels, syrup, and baking soda. Keep it aside for 1 hour so that the the fruits completely absorb the liquid.
Preheat the oven to 162 degree celsius.
Grease a 10-inch-diameter springform pan with butter, next line bottom and sides of the pan with parchmen. Take a bowl and sift both the flours and salt together.
In a separate large bowl, beat the butter and sugar together. Then add in the eggs one at a time and beat again.
Then add in the flour mixture and beat until it is blended. Now stir in the fruit mixture. Then transfer this batter into the prepared pan and cover it with a foil.
Bake this cake 2 hours. Then reduce the temperature to 135 degrees and bake until the tester inserted into the center comes out clean but slightly moist. (This could take about 30 minutes longer.)
Once cooked, transfer it to a rack and remove the foil. Pierce the top of the cake with a skewer, then drizzle 6 tablespoons of rum gradually on top of the cake.
Once it is completely cooled, cut around the pan sides to loosen it.
Serve it warm.