Can a kingsize mattress fit a twin box spring?

No, a twin box spring is not large enough. It would take 2 extra long twin box springs (80 inches in length, as opposed to a regular twin's length of 75 inches), as a kings size mattress is 80 inches long and 76 inches wide (which is twice the width of two twin box springs).

Keep in mind that 76x80 is the measurements of an eastern king size mattress, as a western or "California" king mattress measures 72x84 inches.