To determine the total cost of the pizza for the party, first, we need to find out how many pizzas are needed for 72 people.
Since each pizza serves 6 people, we can calculate the number of pizzas needed as follows:
\[ \text{Number of pizzas} = \frac{\text{Total people}}{\text{People per pizza}} = \frac{72}{6} = 12 \]
Now that we know they need 12 pizzas, we can calculate the total cost by multiplying the number of pizzas by the cost per pizza.
\[ \text{Total cost} = \text{Number of pizzas} \times \text{Cost per pizza} = 12 \times 17 = 204 \]
Therefore, the total cost of the pizza is:
\[ \boxed{204} \]