Did the brother, who swore to his brother that he would take out only one ice cube, commit a breach of his oath, when another piece of ice came out as a result of moving the tray, and is the expiation due upon the one who broke the oath or upon the one who made the oath, given that he is 11 years old?

One who swore an oath before puberty is not obligated to offer expiation for the oath (kaffarat al-yamin (definition)), because the Prophet, peace and blessings be upon him, said: "The pen has been lifted from three: from the madman whose reason is overwhelmed until he recovers, from the sleeper until he awakens, and from the child until he reaches puberty." As for the expiation for an oath, it is obligatory upon the swearer of the oath, not upon the one for whom the oath was sworn, because the swearer is the one who breaks it. It is recommended for the one for whom the oath was sworn to fulfill his brother's oath, unless a harm would result from it, as stated in the hadith (definition) of Al-Bara' bin 'Azib: "The Messenger of Allah, peace and blessings be upon him, commanded us to do seven things... and to fulfill the oath of one who swears by Allah."