This problem is caused by Mopier Mode being enabled by default. The idea of Mopier Mode is to minimize computer and network traffic by sending only 1 copy to a printer equipped with suitable internal memory. That stored copy is then used to produce the multiple copies. Most HP Laser jets do not have suitable internal memory and so only the one copy sent by the computer gets printed.
To disable Mopier Mode:
Click Start
Click Devices and Printers
Right click your Laserjet Printer
Select Printer Properties
Click the Device Settings Tab
Scroll down to the bottom
If necessary, expand Installable Options
Click on Mopier Mode
Select Disable in the selection box that appears
Click Apply
You will now get multiple copies.