Instructions

for the cake

Adjust oven rack to lower-middle position and heat oven to 325 degrees. Grease 9-inch round cake pan, line with parchment paper, grease parchment, and flour pan. Reserve 3 tablespoons sugar. Whisk flour, baking powder, salt, and remaining sugar together in large bowl. Add 2 whole eggs and 3 yolks (reserving whites), melted butter, water, and vanilla and whisk until smooth.
Using stand mixer fitted with whisk, whip remaining 3 egg whites on medium-low speed until foamy, about 1 minute. Increase speed to medium-high and whip whites to soft, billowy mounds, about 1 minute. Gradually add reserved 3 tablespoons sugar and whip until glossy, soft peaks form, 1 to 2 minutes. Stir one-third of whites into batter to lighten; gently fold remaining whites into batter until no white streaks remain.
Pour batter into prepared pan. Bake until toothpick inserted in center comes out clean, 30 to 40 minutes, rotating pan halfway through baking. Let cake cool in pan on wire rack for 10 minutes. Remove cake from pan, discarding parchment, and let cool completely on rack, about 2 hours.

for the filling

Whisk ¼ cup sugar and 1 tablespoon pectin together in small saucepan. Add 1½ cups blueberries and mash well with potato masher. Bring mixture to boil over medium heat and cook, stirring frequently, until starting to thicken, about 2 minutes. Strain mixture through fine-mesh strainer set over bowl, pressing on solids to extract juice; discard solids. Cover with plastic wrap and refrigerate until set, about 2 hours. Rinse saucepan and repeat mashing and cooking process with remaining ¼ cup sugar, remaining 4 teaspoons pectin, 1 cup strawberries, and 1 cup raspberries. Strain and press over separate bowl (discard solids), cover with plastic, and refrigerate until set, about 2 hours.

for the whipped cream

Using stand mixer fitted with whisk, whip cream, sugar, and vanilla on medium-low speed until foamy, about 1 minute. Increase speed to high and whip until stiff peaks form, 1 to 3 minutes.
Using long serrated knife, cut 2 horizontal lines around sides of cake; then, following scored lines, cut cake into 3 even layers. Place 1 cake layer on platter. Spread blueberry filling evenly over top, followed by 1½ cups whipped cream. Top with second cake layer, press lightly to adhere, then spread strawberry-raspberry filling evenly over top, followed by 1½ cups whipped cream. Top with remaining cake layer and spread remaining 1 cup whipped cream on top (do not frost sides). Toss remaining ¼ cup blueberries, ¼ cup strawberries, and ¼ cup raspberries together and arrange in small pile in center of cake. Serve.