Is it permissible to make a birthday cake for a child with the intention of making him happy, even if it's not for holding a party, and is that considered a sin?

In Islam, there are only two Eids: Eid al-Fitr and Eid al-Adha. Any other celebrations, such as the occasions of Mawlid, Laylat al-Qadr, or Laylat al-Isra wal-Mi'raj, are considered innovations (bid'ah) and newly introduced occasions that are not permissible to celebrate or to assist in, whether with money, gifts, or by distributing food and drinks. This is because doing so is considered an affirmation and encouragement of these practices. Therefore, it is not permissible to make cakes or offer gifts on these occasions, even if the intention is to bring joy to children, because it falls under cooperating in sin and aggression.