Foam core? I haven't built that way but many do. I experimented with end grain balsa back in the late 1980s. It turns out to be useful only above the water line. But for that it's good stuff.
Ah. last time I looked Nida Core was more expensive. Carbon fiber honey comb core requires robbing a bank as a first step. Aluminum honey comb core exists but I don't know anything about it.