Preheat oven to 350 degrees and spray four 8" round cake pans with nonstick cooking spray. In the bowl of a standing mixer, combine flax meal and water. Allow mixture to thicken, about 2 minutes. Using the paddle attachment, with the mixer on medium speed, add melted vegan butter, yogurt and almond milk. Add dry cake mixes and blend until mixture is smooth, about a minute. Divide batter evenly between prepared pans, then bake 20-25 minutes, until a toothpick inserted in the center comes out clean. Remove from oven and cool 15 minutes in cake pans before removing cakes.
To make the frosting, blend the vegan butter in a large bowl using an electric blender on medium-high speed. Whip 2-3 minutes, until butter becomes lighter in color and fluffy. With the blender on medium-low speed, slowly add dry frosting mix. Blend until frosting is completely incorporated into the whipped butter. Add water, a few tablespoons at a time, until frosting is smooth and light. You may not need all of the water. Divide frosting into four bowls. Use natural food dye to color each bowl of frosting to desired shade of purple. To make blackberry sauce, place ingredients in a medium sized saucepan over medium-high heat. Bring to a boil and use the back of a spoon to break apart the blackberries into small pieces. Strain sauce to remove seeds, then cool to room temperature. To assemble cake, place one layer of cake onto a large plate or cake platter. Evenly top with lightest shade of purple frosting. Repeat with remaining cake layers and frosting. Top with fresh blackberries, cooled blackberry sauce and powdered sugar. Serve immediately or chill until ready to serve.