On a large, stable cutting board or work surface, slice 1 whole seedless watermelon, making two “slabs” from the center, each about 1½ inches thick.
Slice one “slab” from the center of 1 whole cantaloupe, 1½ inches thick. Slice one more “slab” from the center of 1 whole honeydew melon, 1½ inches thick. Reserve the excess melons for later.
Use a large round cookie cutter or your knife to cut around the seeds/pulp in the center of the cantaloupe and honeydew slabs. Discard.
Stack the melon slabs on top of one another, with the largest in diameter on the bottom.
With your knife straight up and down, cut a circle around the melon stack, slicing just within the rind of the top slab. This should result in 4 equal slabs of melon, with no rind left on any of them. You may want to work in batches, stacking just 2 to 3 of the slabs at a time. Just be sure they are all the same diameter as the smallest slab.
Whip 3 cups heavy whipping cream in a stand mixer with the whisk attachment until soft peaks form. Add 1 teaspoon vanilla extract and 1/3 cup granulated sugar and continue whisking until stiff peaks form, but do not over whisk.
Place one watermelon slab on a serving plate. “Frost” the top with a bit of the whipped cream. Stack the cantaloupe slab on top, then continue stacking and frosting between each layer. After the cantaloupe and honeydew have been stacked, mound a pile of whipped cream in the center to fill in the hole left where you’ve removed the seeds and pulp.
Stack the final watermelon slab on top, mound the remaining whipped cream, and spread it down over the sides of the cake to “frost” your cake.
Top with melon balls (made with the leftover melon) and 1/4 cup blueberries.
Keep refrigerated until serving.