The first try at installing the IDE hit issues:
error while loading shared libraries: libXext.so.6: cannot open shared object file: No such file or directory
The library is installed, so obviously the IDE wants the 32-bit version. I haven't tried to work with 32-bit stuff since Debian went to the multiarch approach, so that led to a new learning experience. Previously one would install ia32 versions of the needed libraries. After a bit of googling, I found that the current approach is (as root, or using sudo):
dpkg --add-architecture i386 # Include 32-bit stuff
apt-get update # Add in the lists of 32-bit packages.
apt-file search libXext.so.6 # Find out what package I need - libxext6 in this case.
apt-get install libxext6:i386 # Add the 32-bit version of thepackage.
Now, the install fails because it's missing libpng12.so.0, so repeat the apt-file search and apt-get install steps for that. In Total I ended up installing libpng12-0:i386, libsm6:i386, libxi6:i386, libxrender1:i386, libxrandr2:i386, libxfixes3:i386, libxcursor1:i386, libxinerama1:i386, libfreetype6:i386, libfontconfig1:i386, libglib2.0-0:i386.
With that, iCEcube2 installs and runs.
Now I can start playing with the eval board when it shows up.