Answer:
The Soviet leadership likely saw the Cuban Missile Crisis as a way to protect their strategic interests and deter a potential US attack on Cuba. They may have believed that by placing nuclear missiles in Cuba, they could deter the US from attempting to invade the island nation and potentially further spreading the communist ideology in the Western hemisphere. Additionally, the Soviet Union may have seen the crisis as an opportunity to test the strength and resolve of the United States and its president, John F. Kennedy.
The Soviet Union also likely believed that the United States had placed nuclear missiles in Turkey which was a threat to Soviet security, so the Soviet Union was looking for a way to balance this threat.
During the crisis, the Soviet leadership was under immense pressure, as they were aware of the consequences of a nuclear war, and were also aware that the US Navy had a naval blockade around the island. They may have believed that the US would not risk a nuclear war over the issue, but it is also possible that the Soviet leadership believed that a nuclear war would be worth it to protect their interests and deter a potential US attack on Cuba.