Actually the item with the most volume is the Reward Chest in the Adventurers' Guild. It says it has a volume of 32 but it can contain more than 32 Reward Container if you kill more than 32 bosses (or other creatures which drop the loot in a Reward Container) within 7 days. But your question is where you can store your items and you can't store your items in there so my answer is following:
The items with the most volume in game is the Lizard Weapon Rack (vol. 25).
Followed by Weapon Rack (Vol. 20) and Armor Rack (vol. 20). Click here to see all of them.
All of these items can be bought for Gold Coins in game and are free available for every player, beside the Lizard Weapon Rack. You can only buy this item from Esrik if you delivered 3 Tomes of Knowledges to Cael.
Almost all cabinets have a volume of 8. The only cabinet with more than 8 is the Cake Cabinet with vol. 10.