If necessary, level cake layers. Place one cake round on cake board (or serving plate). Spread about 1/4 cup buttercream over cake layer. Top with second cake round and repeat adding buttercream.
Top with third cake round. Spread thin layer of buttercream over top layer. Spread thin layer of buttercream around the exterior of cake to seal in any crumbs ("crumb coat"). Chill in the fridge for 15-20 minutes to allow buttercream to set up.
Add another thin layer of buttercream all over exterior of cake. Return to fridge. Keep chilled until ready to serve.
Allow cake to sit at room temperature for 20-30 minutes before serving. Garnish top of cake with toasted coconut. Serve cake slices with remaining coconut syrup.