Is there any sin that cannot be forgive by Allah? Example, the bigger ones alcohol, gambling or adultery, etc.

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

If the person commits a sin and repents from it, then Allah accepts his repentance if it meets the conditions of sincere repentance. Allah Says (interpretation of meaning): {Say: "O 'Ibâdî (My slaves) who have transgressed against themselves (by committing evil deeds and sins)! Despair not of the Mercy of Allâh, verily Allâh forgives all sins. Truly, He is Oft-Forgiving, Most Merciful.} [39: 53].
But if the person dies before repenting, then Shirk, polytheism is the only sin that Allah does not forgive. The other sins are under the Will of Allah. He might pardon him as He might punish him for a period and then let him enter Paradise. Allah Says (interpretation of meaning): {Verily! Allâh forgives not (the sin of) setting up partners in worship with Him, but He forgives whom he pleases sins other than that, …} [4: 116].
Allah knows best.