When scaling with the → Image → Scale command, there is currently no tricubic interpolation. Bicubical interpolation exists of course. When interpolating in three dimensions it looks like it would bicubically interpolate the stack images and then later on cubically interpolate this new stack. (However, I think there is some severe mathematical difference between true tricubic interpolation and this “workaround”.)
The Wikipedia article about the topic ( http://en.wikipedia.org/wiki/Tricubic_interpolation ) gives some overview already. And there was a paper out there by Lekien in 2005 (freely accessible here: http://doi.wiley.com/10.1002/nme.1296 the links in there won't work afaik). The article claims not only that direct tricubic interpolation would be more accurate than consecutive other interpolation methods, it might also be much faster (they claimed 100x, but that's when they used some really high up-scaling, I think). So it might be well worth including this feature.
Googling for “java tricubic interpolation” brings out a couple of pages with the (imO) most interesting ones being: http://www.ee.ucl.ac.uk/~mflanaga/java/TriCubicSpline.html http://www.paulinternet.nl/?page=bicubic
However, I got no experience with programming Java, neither ImageJ macros, so for me it could be a very tedious task and I would highly appreciate if somebody would deem this task worthwhile and would even do some programming on it.