Preheat oven to 350 degrees Fahrenheit and generously grease two loaf pans.
In a large bowl, cream butter and sugar. Add eggs one at a time, beating well after each one. Add vanilla.
Sift flour, baking powder and soda, cinnamon, nutmeg, ginger and salt in a small bowl. Add a little of the flour mixture at a time to butter and sugar until all incorporated.
Drain most of syrup from the sweet potatoes. Mash the sweet potatoes with remaining syrup in a small bowl with a fork. Add to the cake batter and mix well.
Divide batter between the loaf pans and bake for 50-55 minutes or until a toothpick inserted into the center of the loaves comes out clean.
While the cake bakes, make your simple syrup. In a small saucepan, bring water to a boil. Add sugar. Stir until dissolved. Add 3 cinnamon sticks. Let simmer for 30 minutes. Cool until cakes are baked.
Cool cakes for 10 minutes. Cover each cake with about ¼ of the simple syrup. Serve immediately or when completely cool.