Literal translation:
* Наслаждаться жизнью без забот (naslazhdat'sya zhiznyu bez zabot) - This is the most direct translation, but it can sound a bit stiff.
More natural sounding:
* Жить беззаботно (zhit' bezzabotno) - This translates to "live carefree" and is a more natural way to say "enjoy life without worries" in Russian.
* Жить в удовольствие (zhit' v udovol'stvie) - This means "live for pleasure" and conveys a sense of enjoying life to the fullest.
* Жить легко (zhit' legko) - This means "live easily" and emphasizes a sense of freedom and lack of stress.
More poetic:
* Радоваться жизни без тревог (radovat'sya zhizni bez trevog) - This translates to "rejoice in life without anxieties" and is a more poetic way to express the idea.
The best option for you will depend on the specific context.