How did Humanity go extinct in the Revelation Space Universe? Was it the Black Cube Machines?
We simply don't know. The cube tells Bella that humans are extinct but if it tells her how they became extinct Bella doesn't reveal it.
There are several mentions of races becoming extinct e.g. due to the clumsiness of the Musk Dogs or the malice of the Uncontained and it's possible humans fell prey to one of these but it could be an unrelated reason.
As several of the comments to your question have mentioned, Pushing Ice is not part of the Revelation Space universe. On his web site Alastair Reynolds says:
CENTURY RAIN, PUSHING ICE, HOUSE OF SUNS and TERMINAL WORLD are all unrelated standalone novels. I have vague intentions to return to the universes of PI and HOS, but nothing firm ...
That means we should not expect any of the plot devices from the Revelation Space books to be relevant. If Reynolds does return to the Pushing Ice universe perhaps then we will find out what happened to the human race but until then we can only conjecture the reason.