No, Vegas Pro 8.1 is a 64-bit version of Vegas that runs in Vista 64. You could try running it on XP64 but that's not "officially" supported.
> Or the last update of Vegas Pro 8 for XP is 8.0c?
The latest update for any platforms is 8.0c. Vegas Pro 8.1 is actually back-leveled to 8.0b so it has some additional functionality missing that 8.0c has (e.g., new trimmer as a source window fucntions).
XP Pro is a 32 bit operating system, and can talk to 3.2G of RAM, although I think it only allocates about 2G for running programs. This is true regardless of the amount of RAM on the motherboard. XP Pro x64 is a 64 bit operating system, and can talk to more RAM than you can put on any available motherboard. I have 8.1 running on in x64, and I think it reports 4G of RAM available. The neat thing is that when you first load a large file, it loads up extremely quickly because you are using the RAM instead of the hard drive. By the way, my machine is dual boot, so I can start up either in XP 32 or XP 64.
I have 8 GB of DDR2 1100 on my computer - XP64 sees and can use all 8Gb. I turn the preview RAM up to 6GB for Vegas 8.1 and it will use it all - speeds up the rendering noticably on larger more complicated projects.