Note the message to update firmware is not necessarily a bad thing. It doesn't mean it failed or anything. All it is pointing to is that it can't manually set the programmers sck clock speed via software control. However, most USBasp programmers from China, including HobbyKing have an auto-speed feature built in. So just because you are having a failure doesn't necessarily mean it's because of the programmer's firmware version.
If you are having verification errors with programming an ATmega2560, it is because of the larger memory space of those uC. Most ISP programmers do not properly support the larger memory space including these USBasp programmers. You will need a programmer that supports the stk500v2 protocol to address the larger memory space, like the AVRISPMkII programmer from Atmel.
The firmware version of the USBasp programmer can be found from the Details tab in the Device Properties. Version 1.4 is the latest when using usbasp.atmega8.2011-05-28.hex from the USBasp - USB programmer for Atmel AVR controllers - fischl.de site.
