How many total degrees of freedom are in an unreplicated 23 factorial experiment?

In an unreplicated 232^323 factorial experiment, there are 8 runs (since 23=82^3 = 823=8). The total degrees of freedom are calculated as the number of runs minus 1, which is 8−1=78 - 1 = 78−1=7. However, considering there are three factors, each with one degree of freedom, and their interactions (1 for each main effect, 3 two-way interactions, and 1 three-way interaction), the correct total degrees of freedom are 7. References:

Design and Analysis of Experiments by Douglas C. Montgomery.

ASQ Quality Press: The Certified Quality Engineer Handbook.