I'd say the first 20 cubes are pretty fun. I haven't even noticed the cheat menu until 12. Thinking its a later game thing like prestiege or something. Buying new cubes seems like a gamble, as it does not display what's the next level's production. Cube 2 was the breadwinner for a while then 5.
I really enjoyed the animations. The interface slowly growing. Maybe that could be expanded. It starting as a grid and slowly expanding into a large control panel where blinking nonsense of different buttons that help actively progress instead of idling. Maybe integrating the x10 into a feature. It would be a lot like the paperclip game, but that's not a bad comparison.
I didn't feel like 30-60 upgrades introduced a lot of new mechanics. Multiple upgrades being the hypercube increase probably could be one more complicated upgrade with lvl or specific number of level dependencies(the conditions being obscured and revealed when the dependent cube is unlocked, making older upgrades matter more as game progresses.)
Last levels would be great to be something absurd, to actually follow the theme that things become too complicated to comprehend.
For example, right now when the auto magic dice triggers, the screen shakes a little as the aligment moves around. I thought it was a feature and it was a little exciting even. I think more of that should be implemented. Simulate the game breaking as the end nears. There's a bit of a theme with 777 and ricerolls and gambling, so maybe some golden theme? Midas or other greek mythology.
Right now it needs a bit of a direction, and it can stay the same simple mathematic geometry things, but more, to add to the mystery of what the hell is going on. Again, not an "in your face" story, but just hints like comments and the narator in the comments becoming increasingly unsure while trying to explain scientifically what is going to be the effect of the cubes and upgrades as things go deeper.
So i think just expanding on what you have now, more hypercubes maybe sounds about right, but maybe smaller cubes and more dependencies with more rewards, promoting both active and inactive moments, a hypercube that needs to be spun manually, a cube that needs to be aligned in a certain way and progress slowly makes it drift out of aligment, upgradesstabilising it, but never fully.
And maybe a soundeffect closer to 60 square suddently out of nowhere, a droning little noise on the background to make things eerie.
Just embrace the weirdness!~