The Square-2 is a cube-shaped twisty puzzle. It was invented by David Litwin in 1995 as a higher-order version of the famous Square-1 puzzle, and much like the Square-1 it shape-shifts quite heavily when scrambled. The Square-2 has been mass-produced by hknowstore since 2012.
You can think of this puzzle as a Square-1 whose corner pieces were split in half. This makes the puzzle a bit easier to handle and turn since it cannot "lock" like the Square-1 when you have a corner piece blocking the "slice" turn. However, this also gives the puzzle a much greater number of possible combinations, totaling 1.24 septillion! It's also interesting to note that the splitting of the corner pieces allows for two solved positions of this puzzle; One "regular" solved state, and another one with the color scheme flipped (a signle pair of opposite faces swapped in color, for example yellow and white).
A common way to solve this puzzle is by using the "reduction" method. First, decide on the color scheme that you're solving towards (out of the two possible solved states), then pair up the corner pieces to turn the Square-2 into a Square-1, and finally - solve as a regular Square-1.
The Square-2 is not an official WCA puzzle. The world record for fastest solve is unknown at the time of writing, however there are videos floating online showing solves in 20-30 seconds.