Preheat oven to 350°F (175°C). Grease a 9x13 inch baking pan.
In a large bowl, mix together sugar, oil, and eggs until well combined. Stir in grated zucchini and vanilla extract.
In another bowl, whisk together flour, baking powder, baking soda, and salt. Gradually add the dry ingredients to the wet mixture, stirring until just combined.
Pour the batter into the prepared baking pan.
For the crumb topping, combine brown sugar, flour, and cinnamon in a small bowl. Cut in the cold butter until the mixture resembles coarse crumbs. Sprinkle the topping evenly over the batter.
Bake for 45 minutes, or until a toothpick inserted into the center comes out clean. Let cool before serving.