Shulker Box math

Minecraft 1.11 will add Shulker Boxes, which are chests you can break without the items spilling.  Essentialy, they are backpacks in block form.
Let's say you have a single shulker box, with each slot filled with one of a unique item.  For example, slot 1 has a diamond, slot 2 has an iron ingot, etc.
Assuming each shulker box is like this, you can keep a maximum of 27 unique items in a single inventory slot.  In a chest, this means you can keep up to 729 unique items for one chest.
In a 1x2 space, you can use minecart chests to store 3 chests at once.  Taking that into account, 729 * 3 = 2187, so you can have 2187 unique items in 3 minecart chests.
Adding to this, your inventory has 4 rows of inventory slots and an off-hand slot.  2187 + 729 + 27 = 2943, so you can have 2943 unique items in your inventory and 3 minecart chests.

However, it's unlikely you will have 2943 unique items without a modpack, so let's put this to a "practical" use:  diamond storage.
You can store 9 diamonds in 1 diamond block, and diamond blocks stack to 64, so let's take this into account.
9*64 = 576 (one diamond block stack); 576 * 27 = 15552 (shulker box filled with diamond blocks), 15552 * 36 = 575424 (inventory of diamond-block shulker boxes)
15552 * 27 = 419904 (minecart chest filled with diamond-block shulker boxes); 419904 * 3 + 575424 = 1835136 (3 minecart chests + inventory of diamond-block shulker boxes)
So in total, you can store a max of 1,835,136 diamonds using nothing but your inventory and a 1x2 space of minecart chests.