What is the ruling on cutting hair in layers, or a bob, or a cascade, or any short cut for beautification and not for imitation?

There is no harm in cutting hair in a layered, bob, or waterfall style, and the like, provided it does not involve imitating disbelieving women or prostitutes, or men imitating women or vice versa. This is permissible if the intention is for lawful adornment or to reduce the burden of hair and facilitate its styling. The proof for this is what was reported in Sahih (definition) Muslim: "And the wives of the Messenger of Allah, may Allah’s prayers and peace be upon him, would cut their hair until it was like a ‘wafra’ (a large amount of hair reaching the earlobes or shoulders)." This indicates the permissibility of women lightening their hair. And if this is permissible for women, then it is even more so permissible for men under the same conditions.