Orange Buttercream for Hexagonal Wedding Cake

In the heatproof bowl of an electric mixer, combine sugar and egg whites. Set bowl over a pot of gently simmering water, and whisk constantly until mixture is very warm to the touch and sugar is completely dissolved, about 3 minutes (test by rubbing between your fingers to detect any graininess). Attach bowl to mixer stand. Using the whisk attachment, beat on high speed until mixture is cooled and stiff peaks form, 10 to 15 minutes.

With mixer on medium-low speed, gradually add butter, a half stick at a time, beating until completely combined after each addition. Beat in vanilla and liqueur.

Switch to the paddle attachment, and mix on lowest speed to remove all air bubbles, about 5 minutes. Use immediately, or transfer to an airtight container, and store in the refrigerator for up to 3 days. Before using, bring to room temperature, and beat until smooth with the paddle attachment.