Preheat the oven to 350°F (175°C). Grease and flour a 9×5-inch loaf pan or line it with parchment paper.
In a medium bowl, whisk together the all-purpose flour, baking soda, baking powder, salt, ground cinnamon, ground nutmeg, ground cloves, and ground ginger. Set aside.
In a large bowl, beat the granulated sugar, light brown sugar, and vegetable oil together until well combined.
Add the eggs one at a time, beating well after each addition.
Mix in the canned pumpkin puree and vanilla extract until smooth.
Gradually add the dry ingredients to the wet ingredients, stirring just until combined.
Fold in the grated zucchini gently until evenly distributed.
In a separate medium bowl, beat the softened cream cheese, granulated sugar, egg, and vanilla extract together until smooth and creamy.
Pour half of the zucchini pumpkin batter into the prepared loaf pan and spread evenly.
Spoon the cream cheese mixture over the batter layer and spread gently to cover.
Pour the remaining batter over the cream cheese layer and spread evenly.
Using a knife or skewer, gently swirl the cream cheese layer into the batter to create a marbled effect.
Bake for 55 to 65 minutes, or until a toothpick inserted into the center comes out clean or with just a few moist crumbs.
Remove from the oven and allow the bread to cool in the pan for 15 minutes.
Transfer the bread to a wire rack to cool completely before slicing and serving.