None of the publicly released financial data from Microsoft can be used to confirm profit nor loss as of yet, Microsoft has always made financial analysis of their Xbox division ludicrously difficult.
And that's their business, it would be nice to have firm numbers, but it's not in their best interest to make this stuff public. If the news were great, they'd do so, but as we should all know by now, it's DAMN hard to make a profit in the console space unless you have a runaway success AND/OR are brilliant at producing decent sellers at very low costs.
In short, people assuming one way or the other may not have much to stand on, but we can hope for links to confirm more of this as time goes on. IIRC, this is what we know for sure of for Xbox specifically :
OG Xbox : in totality, lost a lot (2-3B negative)
X360 2005-2006 : lost around 3B
X360 2007-2012 : made 100-300M per year in profits
X1 (????, and the numbers would be neutralized somewhat by ongoing XBLG revenue and 360 software sales)
Overall? Almost certainly Xbox as an entity has been a net loser for Microsoft given what we do know.
Microsoft tends to be not great at spending money on launches, and the combined marketing, R&D, kinect, licensing (NFL/Titanfall/etc) costs for X1's launch are probably stratospheric, the only things countering that in a vacuum (comparing X1 expenses to X1 incomes) would be a paper-thin margin on consoles, and whatever they could scrounge from 5M owners with XBLG and software sales.
As the article on Forbes notes, this is not unusual. PS3 is probably profitable by now despite a horrific and similarly mega pricey beginning. If X1 can get to 30-40M install base with a respectable attach rate, along with ever lower costs for licensing, manufacturing, and advertising, I could see X1 turning a profit overall towards the tail end.
About the only thing that's virtually guaranteed is that the X1 on it's sole merits (discarding all X360 related income and expenses) has lost a lot of money so far. That's NOT a surprise honestly. Sony may yet to see profit on the exponentially more successful PS4 to be honest.
Think about it calmly for a minute.
(1)- You start with nothing but a business plan, and thousands of employees ranging from middle-wage to high six to seven figure engineers and executives.
(2)- You invest hundreds of millions into R&D, consumer research, meetings with manufacturers, developers, semiconductor firms, etc.
(3)- You build hundreds of prototypes along the way towards a near-final design, which then goes through various stages of validation, gets handed off with documentation to various teams for software development, packaging design, etc.
(4)- You crank up manufacturing via a variety of international sources, and establish or expand retailer and distribution partnerships. You have to sign commitments to run specific numbers of product through the sources and manufacturers.
(5)- You pay hundreds of millions on marketing and licensing deals with a variety of third parties, and millions more on merchandising materials (display cases, banners, etc)
(6)- All this, and finally you have a product you can sell for $500, whose BoM cost per unit is very close to that. In essence, ALL of the expenses listed above are not included in that BoM cost, only the physical cost to put that stuff in the box. So all the licensing, R&D, employee salaries, advertising, etc are above and beyond the BoM cost.
(7)- Then you have returns, shipping losses (this crate was lost, fell off and was damaged, etc), free product for employees and media, warranty replacements, special discounts (these are compensated back to the retailers if you want to keep a working relationship with that retailer!), and so on. Oh, and pack-in games which have to be compensated for to one degree or another (not $60 cost, but they will want a certain amount, say $20-$25/unit in compensation).
With all of the above, it may cost Microsoft two or three or even four times the BoM cost to get an X1 into a home during the launch period. But after that, things start to get better. Manufacturing costs come down, the initial advertising blitz doesn't have to be maintained to the same level, they don't have to continue to ship X1 hardware to media, return % decreases, and of course, you get more XBLG and game royalties.
I'm skeptical as to when this threshold will be crossed from expense to profit, but it's important to Microsoft that X1 heads into that space before 360 tails completely off. The success of the 360 can mask the shortcomings of the X1 at first, similar to how PS2 gave Sony breathing room while PS3 struggled. If the X1 or PS3 existed in a pure vacuum, both would have had drastically lower chances of continued survival.