Preheat oven to 350°F. Line a 9-inch round or 8-inch square silicone or other nonstick cake pan with parchment paper. Will also make 12 standard-size cupcakes or 36 mini-size.
For frosting: in a blender or food processor combine sweet potato, coconut sugar, unsweetened cocoa powder, cashew butter or almond butter, plant-based milk, vanilla extract, and sea salt. Cover and blend until very smooth, scraping sides as needed. If necessary, add 2 to 3 tablespoons of milk and 1 to 2 tablespoons of coconut sugar to make desired consistency and sweetness. Cover and chill until ready to use.
For cake wet ingredients: in a blender combine sweet potato, maple syrup, vinegar, vanilla, and ½ cup water; cover and blend until completely smooth.
For cake dry ingredients: In a large bowl stir together flour, coconut sugar, and salt. Sift in cocoa powder, baking powder, and baking soda.
Add sweet potato wet mixture to flour mixture. Use 1 tablespoon water to rinse blender to remove any remaining puree and add to flour mixture. Mix just until well incorporated. Transfer batter to prepared pan (s).
Bake 21 to 23 minutes. Cool in pan on a wire rack. Remove cake from pan and top with frosting. Cupcakes: 18-20 minutes. Mini-cupcakes: 12-15 minutes.
Test with a toothpick to see when it is done. Remove from oven and let cook before frosting.