Do you actually have copies of the spam messages sitting in your "sent" box on your gmail account? Or is someone just saying they received spam from your account?
If someone is claiming you sent them spam, get a copy of the message and look at the headers. The last "received" header will identify the server that received the mail and the machine the mail was received from. The other "received" headers will show the servers the message traveled though to reach the precipitant. So you should be able to figure out if the message was actually sent via your gmail account or not.