Preheat oven to 350°F. Grease three 8-inch pans and line with parchment paper.
To make the sweet potato puree, peel and dice the sweet potatoes. Bring a pot of water to boiling and place sweet potatoes in boiling water. Let boil 15 minutes until sweet potatoes are tender. Drain, and mash with a fork or a potato masher. Alternately, you can pulse sweet potatoes in a food processor. Try to get them as smooth as possible.
In a small bowl, combine flour, baking powder, baking soda, salt, cinnamon, ginger, and nutmeg. Set aside for later.
In a large bowl, whisk together oil and sugar. Whisk in eggs, vanilla, and sweet potato puree.
Whisk dry ingredients into wet ingredients. Evenly disperse the cake batter among the three pans. Bake for 23 minutes or until a toothpick inserted in the center comes out clean. Let cool completely.