Japan
No nation dropped an atomic weapon during the cold war. The cold war is not the same as World War 2. Two atomic bombs were dropped on Japan by the US at the end of World War 2. The cold war is called 'cold' because it was not an actual armed conflict. It was a period marked by a conflict of ideologies, propaganda and fear.
The atomic bomb that was dropped on Hiroshima was named "Little Boy." The atomic bomb that was dropped on Nagasaki was named "Fat Man."
The first atomic bomb was dropped on Hiroshima, on August 6, 1945. The second atomic bomb was dropped on Nagasaki, on August 9, 1945.
None. The first atomic bomb was dropped decades after World War 1 finished. Atomic bombs weren't used in war until World War II.
Hiroshima ,Japan during world war 2
1945
2
The only atomic bombs dropped on any nation during a military conflict were the two atomic bombs dropped on August 9 and 6 in 1945. There have been test bombs dropped by Russia and the United States but not on people or cities. Therefore the answer to your question is that there have been no bombs dropped after the space race or since World War 2. The reason is obvious: It causes immense devastation and deaths instantly and for many decades afterward. No nation truly wants to use an atomic bomb. The Atomic Race is basically over and thousands of atomic bombs have been dismantled in the USA and world wide. There are still nuclear missiles around but they are meant for defense against nations who use them as offense against another nation (North Korea is a current treat of this.)
1945 during world war 2
Americans dropped atomic bombs on the Japanese cities of Hiroshima and Nagasaki to defeat them.
The first atomic bombs were dropped during World War 2, initially as tests by the US government, then dropped at Hiroshima and Nagasaki, the only two nuclear devices used as an act of war by any nation. The first atomic bombs were tested on the ground at the Trinity site.