You only cut raspberry canes once they have fruited. With summer fruiting varieties you cut them down immediately after fruiting so the new canes have light and air to make good growth for the next year's crop. With autumn fruiting canes, you leave them until the spring before cutting them, probably because the old canes help protect the crowns, and the new growth doesn't start until next spring.
I'm not sure what your 'white' canes could be. Are you sure this is a raspberry and not another rubus species, such as rubus niveus, known as the Himalayan raspberry or the ornamental r. cockburnianus which has white stems?
These are more in habit like blackberries/brambles and should have the fruiting stems cut down after fruiting.