Preheat the oven to 375º. Lightly coat a 10-cup Bundt pan with oil and dust it with flour.
Wash the unpeeled beets thoroughly and cut into quarters. Steam them until tender, then grate with a cheese grater. Grate each quarter down to the peel (which provides a nice handle while grating), then discard the peel. You should have about 2 cups of grated beets.
Place in a colander and allow the beets to drip while preparing everything else. Using natural sweeteners adds a lot of liquid to the batter, so you don’t want it to be too runny. Note: Reducing the amount of liquid in beets is not necessary if you’re using the original recipe, which calls for sugar instead of liquid natural sweeteners.
Combine the oil, maple syrup, and honey. Stir until well blended. Add the eggs one at a time and beat until fluffy. Add the vanilla extract.
Sift the flour into a large bowl. Whisk in the cocoa powder, baking soda, and salt. Gently stir the flour mixture powder, baking soda, and salt. Gently stir the flour mixture into the batter, until it is just mixed. (Do not over mix—the batter will start to rise before you can get it into the oven.)
Use paper towels and press on top of the grated beets, extracting as much moisture as possible. Fold the beets into the batter, mixing well (but gently), then pour the batter into the pan
Bake for about 45 minutes, or until a toothpick inserted into the center comes out clean. Cool for 30 minutes. Carefully invert the pan onto a place and remove the cake.
Serve when cool.