Set off by a comma, viribus datis
can be read as an ablative absolute. Literally, "strength having been given by him." Generally, an ablative absolute construction in Latin has no syntactic relationship to the main clause, so that "through" isn't strictly speaking correct here. The sense of an ablative absolute is usually temporal--an action that occurred before the main verb, though it may convey a causal relationship.
Here, however, viribus datis
might alternatively be interpreted as an ablative of manner without cum
: "the city was so strong with the strength given by him that . . . ." In the original Livy on which your text is based, the Oxford text and the Teubner text online don't set viribus datis
off by a comma, suggesting that this should be read as an ablative of manner:http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.02.0169%3Abook%3D1%3Achapter%3D15%3Asection%3D7
Ancient Latin texts weren't punctuated--the punctuation was added in printed texts by modern (i.e., Renaissance and later) editors, and there are sometimes differences of opinion as to how ancient texts should be punctuated.
Two other points:Valeo
means "to be strong," not "to become strong."
I think that in
+ accusative here indicates duration, rather than time within which: "the city had a secure peace for forty years thereafter."