Question: "Does Bible prophecy predict that there will be a World War 3 (III, three) before the end times?"
Answer: There is no doubt that world war will be a part of the future. Christ plainly taught that there would be war prior to His return (Matthew 24:4-31). Some hold that He spoke generally of the Church age in verses 4-14 and spoke of the tribulation period starting at its mid-point in verses 15-31. Others believe that Christ spoke of only the seven-year period known as the tribulation in verses 4-31. Though verses 4-14 do seem to be giving general descriptions, they parallel the description given early in Revelation 6, which records details concerning the beginning of the tribulation. Matthew 24:6-7 says there will be "wars and rumors of wars...For nation will rise against nation, and kingdom against kingdom, and in various places there will be famines and earthquakes." Here, Christ makes it very clear that war will play a significant role in the last seven years prior to His return.
To be more specific, the future does hold at least one more world war. There is nothing in Scripture that says there will be only a certain number of world wars. World Wars I and II are not explicitly mentioned in Scripture, nor is a possible third World War. It is only the last war that is mentioned in detail, which allows the interpretation that there may be others before the final conflict.
John the Apostle was shown what the end times would be like, specifically the last seven years prior to Christ's return. Beginning in Revelation 6, he recorded what he saw concerning the future. War is found in this chapter, and continues to be a part of the unfolding events until Christ returns in chapter 19 (Revelation 6:2; 4; 11:7; 12:7; 13:4, 7; 16:14; 17:14; 19:11; 19:19).
Revelation 19:11 says, ". . . in righteousness He [Christ] judges and wages war." Revelation 19:19 says John "saw the beast and the kings of the earth and their armies, assembled to make war against Him (Christ) who sat upon the horse, and against His army." Take special notice that it says the kings of the earth and their armies assembled to make war against Christ. This clearly describes a world war. It also should be noted that the victor in this war is clearly Christ, who seizes the beast/antichrist and the false prophet and casts them into the lake of fire, and the armies that followed them are destroyed (Revelation 19:20-21). So, although there will be at least one more world war, there is no doubt of the outcome—righteousness will prevail as Christ, the King of kings and Lord of lords, defeats all who oppose Him.
It is also worth mentioning at this time that following the 1,000-year reign of Christ, there will be another uprising which could possibly have the scope of a world war. Satan will be bound for 1,000 years and then released. Upon his release, he leads a rebellion among the peoples of the earth. Christ quickly puts down this rebellion and permanently judges Satan, casting him into the lake of fire as He did with the beast/antichrist and the false prophet (Revelation 20:7-10).