In December, 1917, a wire sent from Halifax, Canada ended up in a
private office in Boston, Mass after be routed via Cuba. This was the
only wire to get out of Halifax that day due to a large explosion in
the city. Why would it be routed through Cuba? And is it possible that
the office in Boston that ultimately received the wire did so by
chance rather than because it was the intended recipient? If so, why?

How do you know or where did you read that the cable was "routed via Cuba"?

This additional information could help finding an answer your question.

I don't KNOW it was routed via Cuba; I read it in a book and I'm not
sure it's entirely trustworthy. I believe the message was sent
wirelessly. What I'd like to understand is how the message could
a)travel such a roundabout route and b) end up popping up on a private
machine.