We had a question about whether it was possible to grow Eucalypts by cuttings, given that they grow so readily by seed I did wonder “why?”.
Despite their ready germination, there are a couple of good reasons you may want to, the main one being for the propagation of commercial hybrids and there are a number of hybrids around bred for timber or flower production and the results of growing from seed can be quite variable.
I have seen roots and bits of branch reshoot if they quickly go back into moist ground but cuttings themselves can be tricky, while Eucalypts can form roots from their cambium tissue (which is how long-stem planting works) generally as they age hormones are released from the upper branches which inhibits this activity so as a result cuttings taken from young actively growing branches are more likely to result in success.
This article from the Australian Native Plant Society gives a good rundown on how to do it: http://anpsa.org.au/APOL2007/sep07-s1.html
More information
https://www.publish.csiro.au/BT/BT9700175