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If you're certain of the purchase date, you most likely have an Early 2006 MacBook. The late 2006 MacBook was introduced in November 2006.
This table from EveryMac.com will help you with model specifications
This Wikipedia table gives more specs to compare the many MacBook models, though it does not translate the A1181 designation:
You cannot upgrade it to either OS X 10.7 'Lion' or OS X 10.8 'Mountain Lion', if that is your question.
Microprocessors are not upgradeable.
The newest OS supporting the Core Duo processor installed in your MacBook is OS X 10.6, 'Snow Leopard', and it is still available to order from Apple on CD. It has never been available as a download.
You need at least 1.0GB installed RAM to run Snow Leopard, and 2GB RAM makes performance better.
Full Snow Leopard specs and requirements are found here:
Message was edited by: kostby