if not for the two nukes used in Japan, the war would have continued for probably two more years.
I wrote about this, and linked archival documents from the website of the State Department and the CIA. Also what historians wrote about it.
The Japanese did not surrender due to two nukes. Overall it did not produce an especial impression on them, especially in contrast to the routine fire bombings of Tokyo that they had been experiencing. They were prepared to keep fighting, and the US had no more nukes left after the first two.
What forced the Japanese into surrender, is when Stalin finally honored his promise and opened the Manchurian Front. For two months Soviet forces travelled East from Europe to the Pacific Ocean.
On August 9th, 1945, the Red Army began the Machurian Offensive Operation against the Japanese Kwantung Army. The largest single fighting formation in the Japanese military. Wiki source:
By 1945, the Kwantung Army consisted of 713,000 personnel, divided into 31 infantry divisions, nine infantry brigades, two tank brigades, and one special purpose brigade. It possessed 1,155 light tanks, 5,360 guns, and 1,800 aircraft.By August 16th it was destroyed - with the surrender of 500,000 Japanese servicemen. The next stage was the Soviet invasion of Japan from Sakhalin and the Kurils through Hokkaido.
This meant the imminent entry of Japan into the Soviet sphere of influence, just as with Eastern Europe. America felt it could not allow it, and Japan figured it was better to be occupied by America than by the Russians.
Their impending occupation by the Soviets is what forced Japan to rush a surrender.
Stalin was bitterly disappointed. He had reason to believe that the Soviets were owed territorial compensation for their entry into the Pacific War, as per the Yalta agreements. However, on August 18th, U.S. officials informed Stalin that the American position was clear: Japan proper would be occupied solely by the United States, and any Soviet landing on Hokkaido would be regarded as a breach of agreement.
Within a month, the Americans finally made it over themselves and landed in Japan (September). The rest is history.
Fact is - Russians arrived in Japan earlier than the Americans... somehow.