(Full disclosure: I founded Octeract)
So, a few things here:
Technologically speaking, of course you can (that's the point of a VM), unless a solver is using anti-virtualisation technology, and assuming your hardware supports virtualisation. However, some solver licences tend to be tied to a specific machine/user, so you will need to read the solver's licence carefully to make sure you are not violating the terms of the licence.
Octeract Engine student licence
I can't really comment on other solvers, but for the Octeract Engine student licence you can currently place it and use it on a VM as much as you want, as long as it's you using it on your designated university machine. The only practical restriction of the licence is that you can't use it on a university's cloud. We don't really see this as restrictive, as the student licence supports up to 16 CPUs anyway (see below).
Number of cores supported by the licence
Getting a beefy machine can only help so much, as the student version is up to 16 cores. This is a hard-coded limit that you can't get around, which is true of all multi-core solvers. For high-performance calculations we have academic cluster & supercomputing licences for 96+ CPUs which are commercial. We give pretty lengthy trials though, so simply apply for an Academic Cluster trial licence and we'll sort you out.
Again, I can't comment on other solvers, but since people mentioned performance this is an interesting one. Octeract Engine is a native supercomputing solver - it uses MPI even on one machine, and it will usually work out of the box on an HPC/AWS cluster (unless we need to resolve any funky cluster settings with the university's IT), even for 10,000 cores. What I can say, is that it is the only commercial MINLP solver I know of that natively supports supercomputing. It is installed in a bunch of supercomputers across the world, and we've observed that performance scales linearly with the number of cores, which you can't normally get with a traditional solver. If you are curious, you can see some parallel scaling benchmarks using 170 cores on our website (benchmarks on more cores coming soon!).
The vast majority of solvers are either serial or multithreaded, which means their limit is one machine. This might be the reason you are tempted to build a large VM (I assume you want to build a multi-machine VM), as that could bypass the single machine limitations. However, for most solvers you will not get much out of it because their algorithms are not designed for that level of parallelisation. With Octeract Engine that's not an issue, but you also don't need a VM, a simple cluster will work just fine. One reason why you might not want to use a VM though is that virtualisation can come with considerable overhead, depending on the hardware and the virtualisation software used. One exception here is AWS/Docker VMs. We have tested Octeract Engine on both, and we haven't noticed any performance drops.