cementar

To cement — used literally for construction (cementar un muro, to cement/mortar a wall) and figuratively for solidifying something abstract like a relationship, reputation, or position: cementar una amistad, cementar su liderazgo. The figurative sense is at least as common as the literal one in everyday and journalistic Spanish.

• Los albañiles cementaron la base del muro. — The masons cemented the base of the wall.
• Su victoria cementó su reputación como el mejor del equipo. — His victory cemented his reputation as the best on the team.
• La crisis cementó la alianza entre los dos países. — The crisis cemented the alliance between the two countries.

Confusing cementar with the more general construir or fijar — cementar specifically implies using cement/mortar (or, figuratively, making something as solid as if it were set in cement), not just building or attaching something.