Was there something inherently 'Greek' about the founding of Rome? Did Greek culture infiltrate Rome via conquest, trade? Was there an an acknowledged shared culture that say, Germanic or Celtic 'barbarians' were not part of? When was the start of this culture?
Thanks in advance!
As you may know, Greek polis had many 'colonies' around the Mediterranean, however, Rome was not one of these - although, ever since the founding of Rome, there was much contact between the Latins and the Greeks. This area of study is vast and complicated and as long been debated - the so called 'Hellenization' of Rome. Rome took control of the Balkans/Greek polis generally after the Second Punic War, in the second century B.C. It was during and after this that 'Hellenistic' culture had the largest influence on Rome. Educated Romans were expected to speak both Latin and Greek fluently and generally went to Athens to do so. Contemporaries such as Cicero or Pliny are good examples of 'Hellenized' Romans (although Cicero would often refute such a claim, it becomes fairly obvious in his writings that he was well educated in Greek culture). Perhaps the most visible education was philosophical - Athenian schools such as Platonic, Stoic, Epicurean, etc lasted well into the Roman Empire until they closed around the fifth century. This being said, it is also important to understand that Rome had its own culture as well. The two cultures have often been seen as the same or largely Greek over Roman and only relatively recent studies have began to view the two has separate.
As I mentioned, this is an incredibly large topic. Here are a few readings on it:
Albert Henrichs, Gracia Capta http://www.jstor.org/stable/311309?seq=1#page_scan_tab_contents
Ramsey MacMullen, Hellenizing the Romans http://www.jstor.org/stable/4436211?seq=1#page_scan_tab_contents
Paul Veyne, The Hellenization of Rome & The Question of Acculturations http://journals.sagepub.com/doi/pdf/10.1177/039219217902710601