How did Athens get so strong after the Persian wars?
A peace was made with Persia in 449, so the league became fairly academic, but Athens continued the collections, moving the treasury from neutral Delos to Athens, where Athens spent it as it pleased, including maintaining its overwhellming navy. The league became an empire, and the navy gave it the ability to intervene wherever it wished. The long walls from Athens to its port of Piraeos meant that it could withstand a seige at home, while using its ships to continue collecting funds and harrass any opponent with amphibious raids.