Twist it.
It wobbles back.
Still a real cube.
A real cube underneath. Every cubelet has an integer slot and one of 24 exact orientations. A quarter turn permutes them exactly, so the jelly can never drift.
Your drag picks the turn. The face you press gives two directions on screen; the one closest to your drag wins, and the layer through that cubelet turns around the third axis, the way you pulled.
Soft inside. Each cubelet is a 3x3x3 lattice of springs, pulled toward its exact spot, keeping its volume; a smooth rounded mesh rides on it.
The overshoot is a spring. On release a damped spring swings the layer past the quarter turn and back, and the rest of the cube rocks against it.
Solve plays your moves backwards, tidied first (merged turns, cancelled pairs). All sound is synthesised live: filtered noise and wobbling oscillators.