Pyotr Ilyich Tchaikovsky's "The Nutcracker" is a ballet that he composed in 1892. However, there are some inaccuracies in your request. "The Nutcracker" doesn't have an Opus number 71, and there is no specific reference to "The magical Castle of Sugarmountain" in relation to Tchaikovsky's composition.
Here are some interesting facts about Tchaikovsky's "The Nutcracker":
Premiere: The Nutcracker premiered at the Mariinsky Theatre in St. Petersburg, Russia, in 1892.
Inspiration: Tchaikovsky was inspired by E.T.A. Hoffmann's fairy tale "The Nutcracker and the Mouse King."
Libretto: The libretto (storyline) was adapted by Tchaikovsky's collaborator, Marius Petipa, who also choreographed the original production.
Initial Reception: Interestingly, the initial reception of "The Nutcracker" was not overwhelmingly positive, and it took time for it to become the Christmas classic that it is today.
Characters: The ballet features iconic characters like Clara, the Nutcracker Prince, the Sugar Plum Fairy, and the Mouse King.
Tchaikovsky's Health: Tchaikovsky composed the Nutcracker during a challenging period in his life. He was dealing with personal issues and health problems.
Sugar Plum Fairy Pas de Deux: The "Pas de Deux" in the second act, featuring the Sugar Plum Fairy and her Cavalier, is one of the most famous and beautiful pieces in the ballet.
The Dance of the Sugar Plum Fairy: The famous "Dance of the Sugar Plum Fairy" is known for its use of the celesta, an instrument that was relatively new at the time.
While there isn't a reference to "The magical Castle of Sugarmountain" in connection with Tchaikovsky's Nutcracker, the ballet does take place in the magical Land of Sweets in the second act, featuring the Sugar Plum Fairy's palace.