Make the cake: Preheat the oven to 350°F. Lightly grease an 8- or 9-inch square pan.
Combine the flour, baking powder, and salt.
With mixer, beat egg yolks and sugar until creamy in bowl. Separately in bowl, beat egg whites until they form stiff peaks. Fold beaten egg whites into yolk mixture and fold combined egg into flour mixture, stir enough to wet the dry ingredients.
Pour the batter into the pan and bake for 18 to 20 minutes, or until knife tip inserted in the center comes out clean.
Make rum syrup: In saucepan, combine sugar, cinnamon sticks, lemon zest, lemon juice, and 1-cup water. Bring to a boil over high heat, stir, sugar is dissolved. Reduce heat to low and cook for 7 to 8 min. Add raisins and prunes during final minute of cooking.
Remove syrup from heat and stir in the rum and sherry. Allow syrup to cool for 30 minutes. Remove cinnamon sticks and lemon zest before serving.
Cut cake into 16 squares and arrange on platter. Saturate with syrup and top each with raisins and prunes.