Preheat the oven to 350ºF and prepare your cake pan(s). You can use two 6-inch pans or one 8-inch round or square pan. Spray the pan(s) lightly with oil, then line the bottom with parchment paper for easy cake removal later.
In a large bowl, combine the almond flour, potato starch, tapioca starch, cacao powder, baking powder, and salt. Use a whisk to stir well and break up any clumps.
To the dry ingredients, add in the water, coconut oil, maple syrup, and vanilla. Whisk again, until the batter is smooth. Pour the batter into the prepared cake pans, dividing it evenly if using the two 6-inch pans.
Bake at 350ºF until the cake has fully risen in the center, and is slightly cracked around the edges. This takes about 35 minutes for the two 6-inch cake pans, and 40 to 45 minutes in the 8-inch cake pan. (If using a glass or ceramic baking dish, it might even take a little longer.)
Allow the cake to cool completely before removing from the pan and frosting. This cake will keep well when tightly covered on the counter for up to 24 hours, but for the best shelf life you can store it in an airtight container in the fridge for up to a week.
Video
Notes
I do NOT recommend making any substitutions in this recipe, as gluten-free baking needs to be precise. If you need to use another flour or starch, I'd suggest searching for a recipe that already uses the ingredients you have on hand. In my experience, arrowroot and tapioca starch can usually be used interchangeably, but they won't replace the potato starch in this recipe.
I haven't tested this recipe in a 9-inch cake pan yet, but my best guess is that the cake will bake in 35 to 40 minutes in that size.