Preheat oven to 325 degrees F (165 degrees C). Grease a 9x13 inch baking dish.
In a large bowl, use an electric mixer to beat the eggs until fluffy. Beat in the sugar, oil, and vanilla. Gradually mix in the flour, baking powder, cinnamon, and nutmeg. Fold in the squash. Transfer to the prepared baking dish.
Bake 45 minutes in the preheated oven, until a knife inserted in the center comes out clean.