With iodine: I2? No reaction, I suppose.

With iodide: I-. That should give cis-1-iodo-4-tert-butylcyclohexane.

I'm sorry for making mistake in question. It was iodide I wanted to ask. Thank you for your answer.

if you react the trans bromide with iodide, say in acetone under reflux, you get a Finkelstein reaction and will end up with the cis iodo derivative. This transformation also causes some scrambling; this means that you may also have a small amount of the trans iodide. The mechanism is an SN2 type.

Can you tell me which is the major product? I think it's the SN2 product.

It's the SN2 of iodine you'll get. filled d-orbitals of iodine makes it a better nucleophile (it's also a better leaving group because of the longer C-I bond lenght...). I'd use a large excess, just to make sure it's all converted to the I, but you can easily veryfy this by mass spec (Br = doublets...).

Sn2 means there is inversion, so you'll get the Cis product. Iodine being a soft nucleophile, it will not cause elimination, so I'd expect a rather clean reaction, as long as you don't heat it up too much...

Sodium Iodide in acetone and reflux for 8h. You will get cis(probably) Iodo compound.