Heat oven to 180°C (170°C for dark or nonstick pans). Grease and flour two 20 or 23cm round cake pans.
Make cake batter as directed on box. Add grated lime peel into the batter and fold gently. Pour batter into pans. Bake and cool as directed on box for 23cm rounds.
Reserve 3 whole strawberries for garnish. Cut remaining strawberries into thin slices. Finely chop enough of the sliced strawberries to equal 110 grams.
In medium bowl, beat butter with electric mixer on low speed about 30 seconds to soften, then beat on high speed until fluffy. Add chopped strawberries and powdered sugar; beat on low speed until sugar has been incorporated. Increase speed to medium; beat until frosting is fluffy. Divide frosting into fourths.
With long, sharp knife, split each cooled cake layer horizontally in half. Place 1 layer, cut side up, on serving plate. Spread with one-fourth of the frosting; top with half of the sliced strawberries. Add second layer, cut side down. Spread with one-fourth of the frosting. Add third layer, cut side up. Spread with one-fourth of the frosting; top with remaining sliced strawberries. Add remaining cake layer, cut side down. Frost top of cake with remaining frosting.
In medium bowl, beat whipping cream with electric mixer on high speed until stiff peaks form. Frost side of cake with whipped cream. Refrigerate at least 1 hour before serving. Garnish top of cake with whole strawberries just before serving. Store covered in refrigerator.