From 1525 to 744 BC there were no new Egyptian pyramids constructed. Why did the Nubian dynasty of Egypt (re)started building pyramids?

The empire of Kush (also called Nubia) is a fascinating time in Ancient Egypt history. Ever since the end of the 20th dynasty, after the period so called "collapse of the Bronze age", Egypt struggled with military de facto leaders, weak pharaohs and Libyan rule. Libyans did not invade Egypt, they were assimilated and rose in military ranks until the military rule overshadowed and mixed with pharaonic rule. Thebes, as is usually the case in Egyptian history, rose against the rule of the Lybian dinasty and military action by Osorkon III in 796 ended the Theban rebelion, with considerable blood being spilled in the city of Amun. This action ended a thirty year struggle, and finally Osorkon could rule Thebes uncontested. However, far south, a group of even more devout Amun worshipers was watching this bickering with horror in their eyes. The Kushites (Nubians) adored Amun. No true believer would tarnish the throne and birthplace of Amun this way. The only option was surely to cleanse Egypt of this heresy, take the land of the gods by force and restablish the true worship of the most Egyptian of the gods: Amun. It was time for holy war.

How come the Kushites worshipped Amun so much?

In one of the finest ironies in Egyptian history, Nubia assimilated Egyptian propaganda too well. Since the victories of Thutmosis I and III, Egyptian propaganda found religious justification to the invasion and occupation of Nubia. The main point was the region of Gedel Barkal. This place has a rock formation that resembles a cobra with the white crown of Upper Egypt (a hard sell, make your own conclusions here), and this was enough to claim it as the birthplace of Egyptian monarchy. Thutmosis built a great temple to Amun at the feet of the mountain and made huge efforts to convert Nubians to the true religion. Little did they know this propaganda would come back to bite them, because the worst possible thing happened when Egyptians told Nubians that their land was the birthplace of kingship: they believed in it.

We know of this devotion by titles given to Kushite chieftains like Alara, who would call himself "son of Amun", his successor would claim the title of "King of the two lands". Kush had been independent for a while (efforts to recapture Nubia and its gold mines have been futile for a while at this point) and the slow recovery presented by Thebes following the rule of Osorkon was a prime opportunity to claim Upper Egypt to their "rightful kings", the inheritors of the true, and ancient, Egyptian monarchy. The Nile valley was extremely fragmented at the end of Lybian rule, and many rulers ran to negotiate with the Kushite leader, Piankhi, to keep their thrones in submission to the Nubian overlord. Piankhi would accept these offers by referring to them as "kings" and granting himself the title of "Dual King". Not all leaders complied, and Piankhi advanced his troops to fully take Egypt in 729.

It is only natural that a dynasty using a holy war to justify its rise to power our brim its religious and fundamentalist credentials at every opportunity. When invading Memphis, he would claim:

Look at the southern districts: not a single person was killed there, except for the enemies who blasphemed against god.

Even though Memphis did not open its gates, Piankhi did not raze the city, but instead honored the city's chief god Ptah. This was not a simple conquest, he wanted to purify Egypt. After concluding his conquests, Piankhi would just go back to Nubia and never again set foot in the Nile valley, claiming that his job was done. This would fire up all sorts of independence movements in Egypt (specially, you guessed, in Thebes), and Piankhi's successor Shabaqo would again take over Egypt in another set of campaigns. Politics at the time was a rough business.

And what about pyramid building?

After a compromise of letting some nobles in power and ruling from the south, Kushite rule stabilized and invested in what it really set up for: restoring the good ways in Egypt. I cite here Toby Wilkinson in The Rise and Fall of Ancient Egypt (which is the source for most of this answer):

In another important respect, too, the Kushite monarchy represented a return to the past. With piety to Amun a central tenet of their claim to legitimacy, Piankhi and his successors set out to champion other indigenous Egyptian traditions that had been neglected or overturned by the country's recent Libyan rulers. The Kushites saw as their holy mission to restore Egypt's cultural purity, just as they had saved the cult of Amun from foreign contamination. With active royal encouragement, therefore, priests and artists looked to earlier periods for inspiration, reviving and reinventing models from classic periods of pharaonic history. An obsession with the past soon influenced every sphere of cultural endevour.

Shabaqo took titles from Pepi II, the last pharaoh of the Old Kingdom. His successor took titles from even earlier pharaohs, and nobles started to dust off antiquated and obsolete formulations of titles for the sake of antiquity. Language itself became archaic (or, as they would probably put it, purified), and documents were produced that claimed to be restored from ancient papyrus; carefully crafted to resemble Old Kingdom literature, the 8th century equivalent of the book of Mormon. This was the fabrication of relics of the past, an imagined past of cultural purity that existed only in the minds of Kushite fanatics.

It is, therefore, not at all surprising that Kushite kings would start building pyramids, a practice that was stopped in the beginning of the New kingdom and seen as a relic of the past. As with everything, they added a Nubian sauce to it, Nubian pyramids are shorter and steeper than their Egyptian counterparts. They revitalized Old Kingdom iconography with Kushite images, wall texts and religious texts in a very "old style" fashion with figures of clear African facial features. Nubians also repaired and finished many religious monuments from previous generations of Egyptian rulers. They wanted to be more Egyptian than the Egyptians, and, in a twisted way, there is an argument to be made that they succeeded.