I want to create a magic item that would be basically a lute left by the almighty Pun-Pun. I highly doubt that he would lower his standards to use pitiful materials like adamantium or platinum. I am wondering what is the most expensive material in the world of Dungeons and Dragons that could be used instead.

Materials from Dragon and Dungeon magazines are welcome. Previous editions would be fine as well, but their value would require a conversion to 3.5.

Riverine from Stormwrack is water trapped between carefully-shaped walls of force. It’s fantastically expensive (2,000 gp/lb. for non-armor item), would be preposterously difficult to make into a lute, and is basically indestructible. Sounds perfect for Pun-Pun’s lute.

I cannot guarantee that riverine is distinctly the most expensive special material in the game, but I don’t know of any more expensive.

Star metal at 10,000 gp per pound

Star Metal is the most expensive material I could find. From Forgotten Realms Adventures (2e, p.141):

A typical price was 10,000 gp per pound (22,100 gp/kg)

From Complete Arcane (3e):

Starmetal is extraordinarily hard and is equal to adamantine for all purposes. (...) Creating a weapon of star metal costs 5,000 gp more

For comparison, Mithral is listed as 500 gb per pound under Special Materials. According to Draconomicon (3e) under Trade Goods for calculating dragon hoards, Adamantine is priced the same as Mithral (100 gp for an ore).

So, Star Metal is 20 times more expensive than both materials.

Obdurium (from page 35 of the Stronghold Builder’s Guide) is twice as expensive as Adamantine, but it has 60 hp/inch and 30 points of hardness (both values are 1.5 times that of Adamantine). For a legendary artifact, it seems like a good option. An obdurium weapon costs 6,000 gp more than normal.

Besides the base material, it is also important to consider alloys when determining materials and costs. In particular, Dragon magazine issue 351 (page 45) mentions a special material called “oerthblood” which doubles the hardness of the base material and multiplies the hp by 1.5. For a weapon it raises the cost by 6,000gp.

Assuming lutes are priced similar to weapons, this would make Pun Pun’s obdurium-oerthblood instrument cost an additional 12,000gp for the materials alone. And this isn’t taking into account any non-material features he decided to add into the construction, such as dwarvencraft/elvencraft, skill enhancements, making it a magic or intelligent item, or any of the Artisan Craftsman special properties (described in Dragon Magazine 358).

And for those paying attention, this metal has a hardness of 60 and 90hp/inch.

You're going to have quite a time pricing it but don't look at metals, look at gems. Pun-Pun would have crafted it out of diamond or something of that caliber. Raw diamond can be worked into the desired shape with Stone Shape, nothing comes to mind to fuse pieces together but at his power level that certainly should be possible.

Thinaun

Thinaun is a dark, glittering metal with the strength and weight of steel. It is extremely rare, being found almost exclusively in the Outer Planes, but its true value comes from its unusual property to attract souls. A creature who dies while in physical contact with a piece of thinuan, or a weapon or object crafted from it, will have their soul trapped within it.

Since star metal is only used for improving weapons and armor and is technically to scarce to be made into a weapon, it is very difficult to find a source that could be accurate. Thinaun, however, costs 10,000+ gp at the absolute minimum for a light weapon. I could not find the page, but it is found in the Complete Warrior supplemental rulebook.