Gather all ingredients. Preheat the oven to 350 degrees F (175 degrees C). Grease a 9x13-inch baking dish.

Mix sugar, oil, eggs, and vanilla in a large bowl until well blended.

Combine flour, baking soda, salt, and baking powder in a separate bowl; stir into sugar mixture until well combined. Mix in zucchini.

Spread batter evenly into the prepared baking dish.

Bake in the preheated oven until a toothpick inserted into the center comes out clean, 20 to 25 minutes.

To make the frosting: Blend confectioners' sugar, butter, and cream cheese in a medium bowl with an electric mixer until smooth.

Spread over warm cake. Allow cake to cool completely before cutting into bars.