... or "Would you like (some) cake?" Too many possible translations.
Same here
I went with "Would you like a cake?"
That would be "Ви би хотіли торт?" or even "Чи хотіли би ви торт?" (adds even more politeness)
Is there a difference between Would you like a (whole) cake? and Would you like (some) cake? How would you ask it differently?