It's actually 1.15... x 10^23 or...
115,848,153,000,000,000,000,000 kilograms
That's 115 sextillion kilograms (I may have mathed wrong but I think this is closer? It's using NBT data and the assumption of 32 maximum layers of it)
The maximum weight you can carry in Minecraft is complicated. For starters, ice is better than anything else because the max amount of blocks one water can make is ~537 million blocks^, and ice stacks to 64. Then you use shulkers and stuff. A cubic meter of water is ~1000 KG, so the max weight Steve can carry in two hands is...
45,778,176,000,000,000 kilograms (45 quadrillion kilograms)
- ^ Citation: Alexa real on YouTube*
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Gold is 19.3 times heavier than water. Assuming the pre-1.8 recipe for the enchanted apple which used 8 blocks, one enchant apple weigh 154400 kg. A stack would be 9.88 million kg. A shulker would be 266 million kg. An inventory of shulkers, using all 36 regular slots plus the offhand, would be 9.87 billion kg.
Alternatively, if you do not consider enchanted apples to count, packed ice is 9 ice blocks, and blue ice is 9 packed ice. If blue ice is 81 times denser than ice, then a full inventory of blue ice shulkers would weigh 5.18 billions kg.
using nbt data storage allows you stack chests full of the thing (to 64) in chests and stack that chest in a chest to 64 and put those in a chest and put those in a chest…. so its better than shulkers
You can't do that in survival so it seemed like cheating to me. At that point you can use command blocks and create a block with infinite storage.
The melted ice thing might win out but I thought it was too much of a stretch, considering that most of the water are not source blocks, not full flowing blocks, and there are not enough blocks in a Minecraft world for all of it.