Volumetric Mesh Tips on a Extraordinary Shape Figure

I have a figure of unique shape- four fibers removed from a perfect cube (refer to the images below).

I am new to Cubit, so when I try to apply a simple 3D Hex mesh, the Command Line gives me an error, which I assume is because some locations (which I circled in red below) have funky shapes that make automatic volume mesh to be challenging (refer to the image below).

Mesh Problem

Would you say it’s impossible to apply 3D Hex mesh due to the weird shape at certain locations?
If not, can you provide insights on applying volume Hex mesh on the figure?

I appreciate your assistance.