The Boy in the Striped Pyjamas

An 8-year-old boy named Bruno (Asa Butterfield) lives with his family in Berlin, in Nazi Germany during the Holocaust. He learns that his father Ralf (David Thewlis) has been promoted, due to which their family, including Bruno's mother Elsa (Vera Farmiga) and 12-year-old sister Gretel (Amber Beattie), relocate to the countryside. Bruno hates his new home as there is no one to play with and very little to explore. After commenting that he has spotted people working on what he thinks is a farm in the distance, he is also forbidden from playing in the back garden.
Bruno and Gretel get a tutor, Herr Liszt (Jim Norton), who pushes an agenda of antisemitism and nationalist propaganda. Gretel becomes increasingly fanatical in her support for the Third Reich, covering her bedroom wall with Nazi propaganda posters. Bruno is confused as the Jews he has seen, in particular the family's Jewish servant Pavel (David Hayman), do not resemble the caricatures in Liszt's teachings.
One day, Bruno disobeys his parents and sneaks off into the woods, eventually arriving at an electric barbed wire fence surrounding a camp. He befriends a boy his own age named Schmuel (Jack Scanlon). The pair's lack of knowledge on the true nature of the camp is revealed: Bruno thinks that the striped uniforms that Schmuel, Pavel, and the other prisoners wear are pyjamas and Schmuel believes his grandparents died from an illness during their journey to the camp. Bruno starts meeting Schmuel regularly, sneaking him food and playing board games with him. He eventually learns that Schmuel is a Jew and was brought to the camp with his father.




Prisoner's clothing from Sachsenhausen concentration camp
One day, Elsa discovers the reality of Ralf's assignment after Lieutenant Kurt Kotler (Rupert Friend) lets slip that the black smoke coming from the camp's chimneys is due to the burning corpses of Jews. She confronts Ralf, disgusted and heartbroken. At dinner that night, Kotler admits that his father had left his family and moved to Switzerland. Upon hearing this, Ralf tells Kotler he should have informed the authorities of his father's disagreement with the current political regime as it was his duty. The embarrassed Kotler then uses Pavel's spilling of a wine glass as an excuse to beat the inmate to prove his support of the regime. The next morning the maid, Maria, is seen scrubbing the blood stains.
Later the next day, Bruno sees Schmuel working in his home. Schmuel is there to clean wine glasses because they needed someone with small hands to do it. Bruno offers him some cake and willingly Schmuel accepts it. Unfortunately, Kotler happens to walk into the room where Bruno and Schmuel are socializing. Kotler is furious and yells at Schmuel for talking to Bruno. In the midst of his scolding, Kotler notices Schmuel chewing the food Bruno gave him. When Kotler asks Schmuel where he got the food, he says Bruno offered the cake, but Bruno, fearful of Kotler, denies this. Believing Bruno, Kotler tells Schmuel that they will have a "little chat" later. Distraught, Bruno goes to apologize to Schmuel, but finds him gone. Every day, Bruno returns to the same spot by the camp but does not see Schmuel. Eventually, Schmuel reappears behind the fence, sporting a black eye. Bruno apologizes and Schmuel forgives him, renewing the friendship.
After the funeral of Bruno's grandmother, who was killed in Berlin by an enemy bombing, Ralf tells Bruno and Gretel that their mother suggests that they go live with a relative because it isn't safe there. Their mother suggests this because she doesn't want her children living with their murderous father. Schmuel has problems of his own; his father has gone missing after those with whom he participated in a march did not return to the camp. Bruno decides to redeem himself by helping Schmuel find his father. The next day, Bruno, who is due to leave that afternoon, dons a striped prisoners' outfit and a cap to cover his unshaven hair, and digs under the fence to join Schmuel in the search. Bruno soon discovers the true nature of the camp after seeing the many sick and weak-looking Jews. While searching, the boys are taken on a march with other inmates by Sonderkommandos.
At the house, Gretel and Elsa discover Bruno's disappearance, and Elsa bursts into Ralf's meeting to alert him that Bruno is missing. Ralf and his men mount a search and find Bruno's discarded clothing outside the fence. They enter the camp, looking for him; Bruno, Schmuel and the other inmates are stopped inside a changing room and are told to remove their clothes for a "shower". They are packed into a gas chamber, where Bruno and Schmuel hold each other's hands. An SS soldier pours some Zyklon B pellets inside, and the prisoners start yelling and banging on the metal door. When Ralf realizes that a gassing is taking place, he cries out his son's name, and Elsa and Gretel fall to their knees in despair. The film ends by showing the closed door of the now-silent gas chamber, indicating that the prisoners, Schmuel and Bruno, are dead.

Question: What does Bruno offer Schmuel?
Answer: Cake