"two whole hours" is correct and usable in written English.
You can use it when you want to indicate a relatively long period of time. For example, "I was stuck in traffic for two whole hours."
It took me two whole hours.
We've been together for two whole hours and you haven't talked on your cell phone".
Tonight, the bulky Isbell looks a picture of health as he plays for two whole hours.
Now he is aiming to use his amazing powers of endurance to stay in Exeter for two whole hours.
3.10am: Two whole hours into the Oscar telecast and here it is: the first award for Avatar.
Can my backside, which has been welded to an armchair since lunchtime, withstand two whole hours of Downtown Abbey?
He slept happily and soundly for three whole hours.
Five whole hours in bed, next to my wife.
All in all, the gifts that you gave helped fill four whole hours of Christmas!
Five whole hours after his entrance, the audience is still urging him on.
The point is, Liz has five hours before she needs to take the subway uptown: five whole hours.
