Answer:
I was curious about this question and while many might think the answer is "countless" or depends on whether or not you believe in evolution, it's actually a reasonable thing to calculate as long as you assume some margin of error.
This is not an area of research for me, but for those who do make it their business I've seen estimates ranging from 100 to 110 billion births and this is pretty consistent. You can find this and calculation formulas on the web, what seems to be missing is a simple explanation of why we should believe this number can even be calculated for all time given how much we don't know about how things began.
The important thing to realize is that we have more people living on earth now than ever before and we have reasonably good estimates of the population. Going back in time our population statistics get little by little less precise, but they are reasonably good estimates, with historical support back to say 1,000 AD. Before that, back to say 500 BC there is a healthy mix of historical and archaeological data.
What this shows is that at 1 AD there were about 300,000 people on earth, in 1650 about 1 billion and today over 6 Billion. It is an exponential pattern of growth, meaning if you chart it the graph runs looks like when you pick up a rope from only one end, flat for a while then curving up fast. Curious thing is that this pattern is exactly what scientists observe when an organism is introduced into an environment with unlimited nutrition and limited resistence (predators, disease, etc.) In spite of plagues and tigers, humans since the invention of agriculture have pretty much just populated as if they were following a simple math equation.
The reason it doesn't matter a whole lot whether humanity began with Adam and Eve in 5,000 BC or with a homo sapien introduction 100,000 years earlier is that the population was very low from 5,000 to 1 AD so it had to be lower and lower before that and without agriculture. The potential population in the period we don't know, is vastly outweighed by the population in the period we do know. And what we do know follows a pretty consistent growth pattern for 7,000 years.
So, to recap, humans since the beginning of time: about 110 billion give or take 5 Billion either way.