If I understand correctly, you can boot the corepure64 iso and can download and load corepure64 extensions.
If this is the case, and you'd like to install corepure64 to either usb drive/stick or hard disk then maybe you could answer a couple of questions to make it easier to help:
What medium do you want to install corepuer64 on - usb hd, usb stick or hd?
Is the usb hd, usb stick or hd already partitioned?
Does the usb hd, usb stick or hd partition already have a boot loader and, if so, which one?