This music is very cool, but it also includes some cuteness.
This music is very cool, but it also has some cute aspects.
「この音楽はとてもかっこいいが、どこか可愛さも含む」は英語で以下の文になれます：
１）This music is very cool, but it also includes some cuteness.
２）This music is very cool, but it also has some cute aspects.
例２の方がもっとナチュラルだと思いますが、どちでもいいです。
この音楽 --> this music
とてもかっこいい --> very cool
どこか可愛さ --> cuteness/cute aspects/cute parts
含む --> includes/has
アメリカ合衆国 
