I can't really speak to the Pacific theater, but in the European theater, the Germans made extensive use of POW labor. Most prisoners of war in Germany were used as industrial and agricultural labor, but some POWs were conscripted into forced labor with Organisation Todt, the major German civil and military organization, which also used civilian forced laborers. OT was responsible for many of the major capital construction projects in the Reich and occupied Europe.

The use of POWs as forced laborers began almost immediately after the invasion of Poland, as Polish POWs were put to work as agricultural laborers (as well as being forced to build their own POW camps). By 1941, most Polish POWs had been stripped of their POW status (which protects officers from being forced to work at all, and protects other POWs from being forced to work in certain situations such as military production under the Geneva Convention) and were employed as "civilian" forced laborers.

After the invasion of Western Europe, French, British, and Belgian POWs were also put to work, primarily as agricultural laborers. Early on, the Germans demonstrated a preference to use POWs in work that was considered less sensitive from a national security perspective. Until the invasion of the Soviet Union, POWs of all nationalities were concentrated in agricultural labor. After the US entered the war, American POWs were used in a similar capacity to the other Western Allied POWs.

During Operation Barbarossa, the Germans captured massive numbers of Soviet POWs. Originally, Hitler didn't want to bring Soviet POWs back to the Reich, seeing them as a security risk, and intended to keep them in camps in Poland and the occupied Soviet Union; some Soviet prisoners were brought to POW camps and concentration camps in the Reich, but they weren't used for forced labor at that point. Of course, since they weren't wanted as laborers, the Soviet POWs were allotted almost no food supplies, and a massive number of Soviet POWs (over 2 million) died of starvation and disease by the spring of 1942.

It was only after the failure of Barbarossa that Hitler changed his mind; faced with the prospect of a long war that would tax Germany's industrial capacity, he opted to use Soviet POWs as forced laborers. Within the Reich, Soviet POWs were initially used primarily in agricultural labor and mining, while Western Allied prisoners were used in industrial concerns due to the perceived security risk. This division of labor eroded over the course of the war, as the Germans used large numbers of Soviet POWs and Soviet civilians (Ostarbeiter) as industrial laborers. Similarly, after the Italian capitulation, Italian military internees were also employed as agricultural and industrial laborers.

Soviet POWs were also employed by OT, which was responsible for things like the construction of concentration camps as well as military and civilian engineering projects. One of the most infamous OT projects on which POWs were used was Durchgangsstraße IV, a massive 2,000 kilometer highway across occupied Ukraine, which was intended to supply German troops on the Eastern Front. Construction lasted from early 1942 to early 1944, when it was ended due to the Red Army's westward advance. About half of the more than 110,000 laborers who worked on DG IV were Soviet POWs; we don't know how many of them died, but the death rate was likely very high. OT was also responsible for other tasks like the construction of the Atlantic Wall fortifications and facilities for the V1/V2 rocket projects.

I don't think anyone has calculated the exact breakdown of how many POWs died as a result of forced labor, but based on the existing historiography and my own research, I would estimate that the number for Soviet POWs is well into the hundred-thousands. The Germans frequently falsified death records of Soviet POWs to claim that they died of disease (e.g. "heart weakness" or "edema") rather than dying of starvation and exhaustion due to forced labor. There are thousands of such records just in the files for Defense District VI, which included the heavily industrialized Ruhr region. The numbers for other nationalities, who were generally treated in a manner consistent with the Geneva Conventions, are undoubtedly much lower, although by the end of the war, the Germans were violating the prohibition on using POWs for military labor on a regular basis due to the desperation of their position, and POWs were often killed in Allied bombing raids on military targets, as attested by the postwar investigative records of the Judge Advocate General, which are housed at the National Archives.

In the case of Romania, Soviet POWs were used for forced labor, while American POWs generally weren't. Soviet POWs often faced poor living conditions in Romania, but they weren't subjected to systematic mass killing like they were in Germany (as attested by the death rates; approximately 6% in Romania vs. almost 58% in Germany). Part of the reason for this is that the Romanians were intent on using Soviet POWs as forced laborers from the very beginning; most Soviet POWs were sent to forced labor within weeks. Ion Antonescu shared Hitler's paranoia about Soviet POWs as a security risk, but his hand was forced by economic realities right off the bat. Soviet POWs were mainly used for agricultural labor in Romania, although they were also used on road and railroad construction projects, and were sometimes incorporated into the military labor service battalions that had been established for Jews in 1941. For example, there was a company of approximately 500 Soviet laborers working alongside three companies of Jewish laborers on a strategic highway between Iași and Chișinău in 1943 and 1944. Generally, Soviet POWs were used in a manner consistent with the Geneva Conventions (at least in terms of the work they were doing, if not in terms of conditions), but it's notable that some Soviet POWs were working as manual laborers for the anti-aircraft units defending the oil refining facilities around Ploiești in direct violation of the Conventions. Nonetheless, the death rate for Soviet POW laborers was much lower in Romania than it was in Germany.

I don't know if this was exactly what you were looking for, but hopefully this at least gives a fairly complete picture of the use of POW labor in the Axis POW camp system.

Sources:

Rolf Keller and Silke Petry, eds., Sowjetische Kriegsgefangene im Arbeitseinsatz 1941-1945 (Wallstein, 2013)

Christian Streit, Keine Kameraden: Die Wehrmacht und die sowjetischen Kriegsgefangenen (J. H. W. Dietz, 1997 [orig. 1978])

Ulrich Herbert, Hitler's Foreign Workers (Cambridge UP, 1997)

Wolf Grüner, Jewish Forced Labor under the Nazis (Oxford UP, 2006)

International Tracing Service Digital Archive, Folder 2.2.5.2

NARA, RG 289

[most of the information on Romania came from a book and an article that I wrote, which I'm not going to cite to avoid self-promotion and to avoid identifying myself]