How do I repeat a program in Python with this code?

You can do this using a while loop. So for example:

while True:
   play = input("Do you want to play (type no to stop)?")
   if play == 'no':
      break
   num1 = int(input("Enter first number: "))
   num2 = int(input("Enter second number:"))
   sum = num1 + num2
   if (sum % 2) == 0:
      print(sum, "is Even")
   else:
      print(sum," is Odd")

Put all of this code in a loop and add option to continue/ break before taking input from the user.

while(True):
    option = int(input("Enter 0 to break. Else, continue")
    if option == 0:
        break
    num1 = int(input("Enter first number: "))
    num2 = int(input("Enter second number:"))
    sum = num1 + num2
    if (sum % 2) == 0:
       print(sum, "is Even")
    else:
       print(sum," is Odd")

print('entry "quit" when you want toe terminate the program')

# infinite loop
while 1:
    # input validation
    try:
        num1 = int(input("Enter first number: "))
        num2 = int(input("Enter second number:"))
    except ValueError:
        print('Please entry a number')
        print()
        # continue would restart the while loop
        continue
    if(num1 == 'quit' or num2 == 'quit'):
        # break will terminate the while loop
        break
    sum = num1 + num2
    if (sum % 2) == 0:
       print(sum, "is Even")
    else:
       print(sum," is Odd")

You can always nest these statements in a while loop and break on some condition.

def process_results():
    num1 = int(input("Enter first number: "))
    num2 = int(input("Enter second number:"))
    sum = num1 + num2
    if (sum % 2) == 0:
        print(sum, "is Even")
    else:
        print(sum,"is Odd")


def get_choice():
    print("Enter R to run program or Q to quit:")
    choice = input()
    return choice


def main():
    while(True):
        choice = get_choice()
        if choice == 'R' or choice == 'r':
            process_results()
        elif choice == 'Q' or choice == 'q':
            print("This program has quit")
        else:
            print("You must enter R to run program or Q to quit")
main()