Sigma Notation to Discrete Values

Question

I was reading the top voted answer for What is the average of rolling two dice and only taking the value of the higher dice roll?

I ran into the following $$\begin{align*} &=\frac1{18}\sum_{k=1}^6k^2-\frac1{36}\sum_{k=1}^6k\\ &=\frac{6\cdot7\cdot13}{18\cdot6}-\frac{6\cdot7}{36\cdot2}\\ \end{align*}$$

I want to understand how this transformation from sigma notation to discrete values without writing out the entire series is done, what should I study?

If it's simple enough to explain feel free to just explain it in the answer, otherwise I'm happy to educate myself with Khan Academy, Brilliant.org or somewhere else. I just don't know what to look up

Answer 1

https://en.wikipedia.org/wiki/Square_pyramidal_number: $$\sum_{k=1}^n k^2 = \frac{n(n+1)(2n+1)}{6}$$ https://en.wikipedia.org/wiki/Triangular_number: $$\sum_{k=1}^n k = \frac{n(n+1)}{2}$$