Just install and open Briz LUT Converter, click the "Convert LUT to ICC profile" item from the top menu.
Then you should place the created .icc file into the folder:
PC
C:\Program Files\Phase One\Capture One 12\Color Profiles\Common
or
C:\Users\UserX\AppData\Local\CaptureOne\Color Profiles
Mac
Users/UserX/Library/Colorsync/Profiles
The Library folder is hidden. To open it, make sure you are in the Finder, hold down the Option key, and then choose Go > Library.
Restart Capture One and the ICC Profile will be available:
Please note that trial version cannot convert LUTs to ICC profiles.
To make sure that the full version will work for you, you can use this examples:
BrizLUT2ICC.zip
(the archive contains *.icc files converted from *.cube files by Briz LUT Converter as well as original *.cube files for comparison)
Please feel free to contact us if you have any questions regarding this software.