No, Strong Gust will not do 180 damage after being used twice in a row. Strong Gust's base damage is 60, and its effect is that the pokemon using it's Strong Gust attack does 60 more damage during the next turn. It does not imply that it does 60 more damage than it did during that turn, it just says "60 more damage." Even if you attacked for 120 after using it once, it will still be 120 the third time. The base damage is always 60, and the effect makes it do 60 more the next turn, adding up to 120, regardless of how many times you used the attack.