Fuze - The prefix 76A tells us your tractor is a D6C with 74" track gauge, is fitted with a powershift transmission, and it was built in the U.S.
The 3340 number is the sequential build number (serial numbers started at 76A0001 for the 1st tractor off the assembly line), and S/N books tell us 76A3340 was built in 1965 (76A2107 to 76A3593 were built that year).
The engine is indeed known as the D333, it is primarily identified by its bore diameter, which is 4.5".
Your tractor and its engine share the same serial number. With later model Cats after about 1971, the engines got a separate serial number.
You buy the D6C Service Manual that has on the front cover, "For 74A and 76A models". 74A is the Direct Drive transmission version, and both types of transmissions are covered in the manual.
IPD can provide a good quality aftermarket engine overhaul kit for your engine.
When overhauling this engine, one of the primary areas where you need to exercise great care, is in cylinder head installation.
There are brass ferrules that are fitted with a rubber compression seal around a centre projecting flange of the ferrule, between cylinder head and block.
These ferrules contain coolant directors that must be oriented correctly upon installation. There is an arrow stamped in the top of the block to guide you, and the manual describes the ferrule orientation procedure.
In addition, when replacing the cylinder head onto the block, great care must be exercised when lowering the head, that the head is perfectly aligned and lowered evenly onto the ferrules, to avoid crushing them via misalignment - which can happen if the head is lowered too rapidly and unevenly.
Accordingly, a mechanical lowering method that can be carefully controlled, is a far better system to replace the cylinder head, as compared to simply lowering the head on by hand.
Having said this, I have replaced numbers of D333 cylinder heads by hand with success - but had at least one that I recall, that ended up with an accidentally-crushed ferrule - which caused a leak, which necessitated head removal again!