Should I consider "four times the work" as one noun? And can I say "the work of four times" instead?
"Four times" here is actually an adjective describing the noun "work", meaning that the amount of work has been multiplied by four so there is four times as much work. The only noun here is "work". It would sound unnatural to change this to "the work of four times", but you could say "the work has increased by four times", or "the work is four times as much" instead. Ex: He has been to three times as many countries as I have.