Greetings, Sir Christian. As of now, we are going to solve PROBLEM SET 6B—MATA. For this problem set, we have to prove that 1 cubed + 2 cubed up until n cubed is equal to 1+2 up until n squared. But before proceed on doing the base case, we will replace 1+2 up until n squared with n times n + 1 over 2 since it is the equivalent formula when talking about Arithmetic Sequence, then squared it because of the exponent 2. So this becomes 1 cubed + 2 cubed up until n cubed is equal to n times n + 1 over 2 squared. For the base case, we have to show that n = 1 n cubed is equal to n times n + 1 over 2 squared. For every element of n in the current equation will be replaced with the given value, 1. This becomes 1 cubed is equal to 1 times (1 + 1) over 2 squared. Then we'll simplify it one at a time. 1 is equal to 1 times 2 over 2 squared. 1 is equal to 2 over 2 squared. 1 is equal to 1 squared. 1 is equal to 1. Therefore, for every element of n is true at 1.