One of my favorite things to do as a child was to help my mom make shaped cakes (rockets, numbers, animals, etc) out of regular cake pans. I loved the puzzle aspect, the challenge of using every piece of cake, the final result that looked nothing like what we started with.
While there are obviously countless combinations of cake pans one could use to form a six and a zero, I used an 8” square pan (used once) and an 8” angelfood cake pan (used twice), putting about five cups of batter, or one cake mix, in each pan.
If you didn’t have a ring, you could also use a round pan with a small can (both ends cut off) placed at the center to form a nice clean hole during baking.
After baking one square cake and two ring cakes, I trimmed all three to be 2” tall. Here are paper cut-outs of the cakes…
(When making odd-shaped cakes from regular-shaped pans,
I often practice first by cutting out papers in the shapes of my baked cakes, then cutting them up and rearranging them until I get the new shapes I want. I keep the tape handy… or am ready to cut out additional shapes when I completely mis-cut the first ones.)
To show you the “big picture” first, I cut the cakes like this…
…to form this:
If you want more details of the cake cutting, read on…
Measure the width of one side of a ring. Then from the square, cut two tall rectangles equal to the width just measured. 
To make the “zero,” cut one of the rings and one of the rectangles in half. 
Then move the ring halves apart, and put the smaller rectangle pieces in between. And there’s the “zero.”
To make the “six,” from the remaining ring, cut off and set aside an “offset quarter.” (The vertical cut is to the left of the exact middle, tangent to the inner circle; the horizontal cut is below the exact middle, and also tangent to the inner circle.) 
Place the remaining tall rectangle into the empty section, then cut away the excess at the top, shown in darker pink below.
Moving the “offset quarter” piece into position, cut away the remaining little point, extending the curve of the quarter piece.
So there’s the “six.”
Put them together, add some frosting, etc. and you get this.
Some other notes and hints:
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I highly recommend that you
make a custom cake board for each number instead of putting them next to each other on a larger surface right away. This will allow you to move and work on each cake independently; otherwise, it’ll be
very difficult to nicely frost the areas of the numbers that are nearly touching each other (the right side of the “6” and the left side of the “0”).
To make the boards: put each cake on a piece of cardboard, trace around the number about 1/4” from the sides of the cake (to leave room for the frosting to be added), then remove the cake and cut out the cardboard shape, including the inner hole. (I also covered mine with foil.)
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Putting the cake pieces back on the cardboard, I slathered some frosting between each cut – like sticking bricks together. Then I gave each number cake a
crumb coat and a final coat of frosting. I also added designs to the sides, particularly the sides that I knew would be unreachable after I put the numbers next to each other. Finally, I piped the border along those sides as well (visible in next photo).
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Since I couldn’t fit my pastry bag in the holes from the top, I piped a border along the bottom edge of the holes by coming in from underneath. You’ll probably need someone else to hold the cake up…
…someone trustworthy! : )
