These are mem cakes. You can obtain these by passing the various tests within the underground facility. From what we can determine, these cakes are formed by compressing one’s memories into physical form. If you’re able to collect some of these, show them to Iso Padre. He’ll be quite delighted!
— Squid Research Lab
Source: Splatoon’s Tumblr.
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And if you’ve already got yours, click on Splatoon 2 for everything you need to know about the game. 😀