Anyone wanting to read the principle speech that Bush gave to the UN can look the text up at the link below.
Bush did not claim that Iraq had nuclear weapons. He outlined how Iraq had had a program which was dismantled in part but the main issue was the ten year failure to comply with the UN inspections and settlements of the first Iraq war in a manner that let the world know it was a safe and compliant nation.
http://www.cbsnews.com/news/text-of-bush-iraq-speech-to-un-12-09-2002/
It was the repeated failure to comply and the inability of the world to ascertain if WMD programs were proceeding that led to the declarations from the UN.
During the questioning of Sadam after capture it became apparent that he wanted everyone to think he had a more active program to keep other Arab nations and Iran in fear of his possible abilities. That is why he didn’t comply.
The older WMDs were hidden and sent to Syria but what was found was from that earlier period and never met the media’s standard for the narrative that THEY adopted about the war. A narrative the Bush administration never outlined in a manner that the media later knocked down as a “straw man” argument.
I remember clearly that WMD was only one of the reasons for invasion. Saddam needed to be gotten rid of. He was removed successfully and everyone was better off until Obama refused to allow a residual force.