There is no conventional way to cut a circle cake into eight equal pieces with three cuts. It takes four standard cuts. However, creative thinking leads to at least a couple unconventional approaches. One is simpler and more accurate than the other.
Cut the cake in half vertically
Cut the cake in half from top to bottom through the center. This cut leaves two equal halves on the left and right
Cut the cake in half horizontally
Make a separate cut horizontally across the center of the cake. This cut leaves four equal pieces, or wedges, of cake.
Stack the wedges
Stack the four wedges one on top of the other so it results in a four-wedge-tall structure. You may need to brace each side with a box or some other object to hold them steady.
Make a cut through the center
Each wedge has a semi-circle on the back and a pointed edge on the front. Cut down through all four wedges from the pointed edges to the center of the back semi-circles. Start the blade at a 45 or 60 degree angle at the front of the top piece, and move it down through the wedge. Continue pushing the knife straight down through the four wedges. The four wedges become eight smaller pieces.