Preheat your oven to 350°F (175°C).
Grease and line three 8-inch round cake pans with parchment paper.
In a large bowl, whisk together the flour, granulated sugar, light brown sugar, cocoa powder, hot chocolate powder, baking powder, baking soda, and salt.
In another bowl, mix the dairy-free buttermilk, warm water, vegetable oil, dairy-free yogurt, and vanilla extract until smooth.
Add the wet ingredients to the dry ingredients, mixing until just combined.
Divide the batter evenly among the prepared pans.
Bake for 25-30 minutes, or until a toothpick inserted into the center comes out clean.
Allow the cakes to cool in the pans for 10 minutes, then transfer to a wire rack to cool completely.