Preheat the oven to 350°F. Grease a muffin tin or line it with paper liners.
In a large bowl, mix the cucumber, eggs, oil, vanilla, and sugar until evenly combined.
Add the flour, baking powder, baking soda, cinnamon, and salt all at once. Stir just until no dry flour is visible.
Fill the muffin cups about three-quarters full. For loaf pans, fill each pan about halfway full.
Bake muffins for about 20 to 25 minutes, or until the tops spring back lightly and a toothpick comes out clean or with a few moist crumbs. Bake loaves for about 1 hour, checking the center carefully.
Let the muffins cool in the pan for about 5 minutes, then transfer them to a wire rack before storing or serving.