I'm looking to optimize a simple sum calculator used in Project Euler+. The premise is simple: Find the sum of all the numbers divisible by 3 or 5 under X.

At first I did it like so:

def main(testCases):
    final_answer = []
    for x in range(testCases):
        answer = 0
        test = long(input())
        for num in range(test):
            if (num % 5 == 0 or num % 3 == 0):
                print(num)
                answer += num
        final_answer.append(str(answer))
    print('\n'.join(final_answer))
main(input())

Which worked alright. Then I realized it couldn't handle anything like 10,000,000,000 at all, which was bad, so I tried:

def main(testCases):
    for x in range(testCases):
        answer = 0
        num = input()
        
        Temp = (num - 1) // 3
        answer += (Temp * (3 + Temp * 3)) // 2
        Temp = (num - 1) // 5
        answer += (Temp * (5 + Temp * 5)) // 2
        Temp = (num - 1) // 15
        answer -= (Temp * (15 + Temp * 15)) // 2
        print answer
main(input())

Which was way faster / capable of giant numbers. However, it seems really ugly and unoptimized, but maybe it's in my head. Can anyone help me optimize my answer?

Sample

Input:

2
10
100

Output:

23
2318