Add sugar to small saucepan. To keep sugar crystals from forming along sides, carefully pour water along sides of saucepan so that sugar no longer touches sides. Over medium low heat, without stirring, begin heating mixture until it starts to boil. Clip on candy thermometer and continue to cook until syrup reaches 235 degrees.
At this time, begin whipping egg whites at medium high speed in mixing bowl. Egg whites should reach stiff peaks at the same time the syrup reaches 245 degrees. If they are not there yet, remove syrup from heat and hold until egg whites are at stiff peak stage.
Slowly and carefully pour sugar syrup down the side of the bowl where the whites touch the side, being careful not to let the syrup hit the whisk attachment. Continue to whip the meringue until the sides of the bowl are cool to the touch (this could take 5-10 minutes).
Begin adding the butter, a few tablespoons at a time. Mixture will look curdled about half way through adding the butter, but just continue to slowly add the butter. When mixture comes together into a smooth and creamy buttercream, stop adding the butter. Sometimes it takes only 3 sticks, but sometimes, depending on the ambient temperature of the room, it could take up to 4 sticks.
Spread or pipe buttercream onto cupcakes. If there is any left over, refrigerate for about one week or freeze for 3 months.