"She really likes the cake."
Translation:A lei piace davvero la torta.
I presume that "davvero", or "really", is usually used to modify a verb. I.e. "He really likes it."; "They really make it fun."
While, "molto", or "very", is often used to modify an adjective. I.e. "It is very heavy."; "They are very nice."
Although, in English, we often use "really" too to modify an adjective as an emphasis.
It's just my opinion, though. Please correct me if I'm wrong. Grazie. :)