.250 diameter 6.125 inches deep.

Like butter.  Parabolic drills are magic.

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I've done some long drilling before, too. Personally, I would've started with a stub (screw machine) bit. Then, moved to a jobber and finished w/ a taper length. Depending on how accurate and straight you needed such a hole.

Did it come out the other end centered?

I like parabolic drills a lot.

It's a blind hole in bar bar stock. Yes it stayed centered. This is a stepped hole that fits over a tapered mandrel. The first operation is this .250 x 6.125 hole. I have done this an number of times and when properly set up with the right feed on the carriage it drills dead on center.

What I have noticed is that the feed pressure has alot to do with the result, to light and holes isn't round to heavy  and the hole isn't straight.

I have also had the best results using a center drill and then moving to this drill. Working up with stubby drills did not produce better results.

Suspicious lack of lubrication represented in those pictures.

Well it's aluminum and wd-40 is clear...