215/65 R15 Tires on 15x6 Rim?

Convert to inches. 215 mm is 8.46 inches. So a six inch rim is just two inches narrower than the width of the tire at its widest. It will work but not recommended. A 215 mm tire should really be mounted on a 7 or 7.5 inch rim.

The bolt pattern is irrelevant when it comes to fitting tyres to rims. The diameter of the tyre has to match the diameter of the rim first off. Your tyre and rim are both 15" so that's a good start. But a 6" rim is a bit narrow for a 215 tyre. A 215 really wants a 7" rim. Your 6" is OK, but right on the limit.

No, the minimum width recommended for 215mm (8.5") wide tires is 6.5".

That is because my winter tires are the 215/65R15 size. Originally they were from another car and when they were put on the Cruze I had to buy new rims (since it was a different bolt pattern). The current rims are X43557 rims (5x105 and 6'' wide). The problem is they are getting really rusty again, even though I painted them less then two years ago. So at this point I would rather just get new rims than have to re-paint. These must have been really cheap rims, since I know lots of people with steel rims that are much older and they have very little rust.

A 215/65R15 sized tire has a wheel mounting range of 6-7.5". So it would fly but barely.

But your question begs another question. Why do you want to use 15 inch diameter wheel on a car which has 16" wheels on a base model?