Something that is costly to maintain and generally of little utility is considered a "white elephant". These were prized animals for their rarity in the wild but kept by the wealthy as indications of their wealth. As they often came to be seen as far more costly to maintain than their actual worth they were given as backhanded gifts to others. Killing a white elephant would be considered a cruelty, as would setting it free in unfamiliar terrain. It would eat plenty and live for decades, potentially bankrupting someone of lesser wealth. Elephants are used as pack animals, and done so at a profit, but this would not be something one would expect a rare white elephant to do.
It sounds like what you seek is a palace that is made of something rare, but also has a high maintenance cost. Perhaps I'm not being very helpful as I cannot think of anything specific. Just keep in mind that any large building will require considerable maintenance and that alone can make it a white elephant.
Another thing to think of is what is considered the most valued place in an empire. I'll use America as an example. For many in the world getting to America, even as a visitor, is considered something to be valued since this is seen as something approaching an "empire" of great wealth and power. Then consider that getting to a center of great power inside the "empire", which makes getting to the US capital what people aspire to. Then comes getting to the White House, a highly guarded "palace" of sorts. Then the "center" of that is the Oval Office. This is a place people want to visit and that's because that's the office of the President of the United States. Just the fact that the palace contains the emperor makes it valuable no matter what it is made of.
A similar thing can be said of a religious example. 238
People will want to visit Rome as that's a pilgrimage to see many holy sites. Inside that is Vatican City. Inside that the Sistine Chapel. And that's valued because it's where the Pope and College of Cardinals meet, as well as being a place bearing incredible works of art going back centuries.
A place of awe doesn't have to be a white elephant, or a seat of power for someone of political and/or religious influence. It can bring awe out of it's utility, quite the opposite of a white elephant. People desire to visit places that are examples of engineering marvels. They will want to see hydroelectric dams, military fortifications, nuclear power plants, large telescopes, particle accelerators, and tall towers. Which takes me back to the examples of DC and Vatican City where people seek out information that few can know or see, contained in books or the minds of the inhabitants. The libraries and museums that contain this information is valued.
Consider the value of information. The value of the instruments of science or espionage. A place like DC, Vatican City, or other capital cities will not only contain the "palace" but also information, large engineering projects for creating and protecting this information, and the people in authority of it all.
One such engineering feat that would bring awe could be something like the one and only known stable fusion reactor in the empire. This would be of considerable value not just in the power output to keep the capital complex lit and heated but provide power for weapons, growing food, powering industry, and so forth. This would be something that few would be allowed to even see out of concern for keeping the secrets of how it works and to defend it from sabotage. If there's a rare material to be sought then perhaps it's the plasma within an artificial star that powers the center of an empire.
Having a single such reactor is likely something no empire could rely on as that one point of failure would make too much of a target. Perhaps the palace sits upon the largest of them, or the first of them. 111