The capital city of West Bengal is Kolkata, also known as Calcutta. Here is a detailed explanation of this answer:

Kolkata - The Capital City of West Bengal:
Kolkata is the capital city of West Bengal, a state located in the eastern part of India. It is the cultural, commercial, and educational center of the state and is one of the major cities in the country. Kolkata is situated on the eastern bank of the Hooghly River and is known for its rich history, vibrant arts and literature scene, and colonial architecture.

Historical Significance:
Kolkata has a significant place in India's history. It was the capital of British India from 1772 to 1911 and played a crucial role during the Indian independence movement. The city witnessed several important events, including the partition of Bengal in 1905, the Swadeshi Movement, and the formation of the Indian National Congress.

Cultural Hub:
Kolkata is often referred to as the "cultural capital of India" due to its deep-rooted cultural heritage. The city is known for its love for art, music, literature, and theater. It has produced renowned poets, writers, filmmakers, and artists who have made significant contributions to Indian culture. Kolkata is also famous for its Durga Puja festival, which is celebrated with grandeur and enthusiasm.

Economic Importance:
Kolkata is a major commercial and financial hub in eastern India. The city has a diverse economy, with industries ranging from textiles, jute, and tea to steel, pharmaceuticals, and information technology. It houses the headquarters of several major companies and is an important trading center. The Port of Kolkata, located on the Hooghly River, is one of the oldest and busiest ports in India.

Educational Institutions:
Kolkata is home to some of the finest educational institutions in India. It houses prestigious universities, including the University of Calcutta, Jadavpur University, and Presidency University. The city has numerous renowned schools, colleges, and research institutes, making it a hub for education and intellectual activities.

In conclusion, the capital city of West Bengal is Kolkata. The city's historical significance, cultural heritage, economic importance, and educational institutions make it a significant and vibrant city in India.