I recently got three new baby male rats, and I needed a new cage for them. I knew that Martin's rat cages are well regarded, so I did some research on them. I solicited recommendations from a pet rat owner list (the "Ratlist"), and performed a number of calculations and comparisons of my own.
I calculated the amount of floor space in each cage by adding together the areas of the floor and shelves (not ramps). This measurement meant more to me than the cubic dimensions and volume of a cage, as my rats use the floor and shelves far more than they use the walls. I then calculated the price per square inch to get an idea of how much floor space I was getting for my money. I considered only the powder coated version of each cage.
In general, the consensus of the many replies sent to me was to get an R680 or larger cage. The four favorite cages were the R680 and R685, and the tall R690 and R695. These would all be large enough for three boys. The smaller R670 also got positive reviews, as did the larger R699 Ruud cage. Here's the breakdown:
Cage number Cage name Scale Diagram (1/8 inch = 2
in) Dimensions (W x D x H) Shelf arrangement Floor space (in^{2}) Price (powder coat) Price/in^{2} Special features Summary R670 The Rat Cabin 24 x 14 x 24 Two 1/3 shelves 560 in^{2} $56 $0.10 per in^{2}  Several people own and like this cage,
and find it quite roomy enough for 23 males, especially if
the rats get a great deal of free range time outside the
cage. It has room for hammocks, tunnels, a wheel, and toys,
and it fits easily in a bathtub for cleaning. Others
consider it a bit on the small side and prefer something
larger. It is the cheapest cage on this list, but at $0.10
per square inch, its floor space is actually the most
expensive. R680 The Rat Lodge 30 x 18 x 24 Two 1/3 shelves 900 in^{2} $74.75 $0.08 per in^{2} Large door This cage has larger dimensions than the
R670, but the same twoshelf layout. The added width and
depth allow for over 60% more floor space than the R670
(900 vs. 560 in^{2}). People also like the R680
because of its large front door, which lets you remove large
cage furniture like the Wobust Wodent wheel without
dismantling the cage or the wheel. The R685 and the R690
series cages have smaller doors that do not let you do
this. R685 The Rat Retreat 30 x 18 x 24 One full second floor 1080 in^{2} $90 $0.08 per in^{2} Fliptop lid The R685 has the same external
dimensions and cubic volume as the R680, but it has a
different internal layout: it has a full second floor
instead of two shelves. Because of this different internal
layout, it has 20% more floor space than the R680: 1080
in^{2} vs. 900 in^{2 }, and is priced
accordingly. Its fliptop lid allows easy access to the
second floor. R690 The Rat Tower 24 x 14 x 36 One full second floor Two 1/3 shelves 896 in^{2} $76.75 $0.09 per in^{2}  The R690 has the same small tray size as
the R670, but is a foot taller and has an additional full
second floor. Because of this additional floor, it has 50%
more floor space than the R670. In fact, it has almost
exactly the same floor space as the R680. It has 20% less
floor space than the R685. Its special advantage is that
because of its smaller tray size, it fits into a bathtub,
making cleaning easier than the R680 series or the R695.
Its smaller size also makes it easier to handle than the
R695. R695 The Rat Skyscraper 30 x 18 x 36 One full second floor Two 1/3 shelves 1440 in^{2} $99.50 $0.07 per in^{2}  The R695 is a tall cage with the same
larger tray size as the R680 series, but it has the full
second floor and two 1/3 shelf layout of the R690. The
result is more floor space: 1440 in^{2} , which is
60% more floor space than the R690, and 33% more than the
R685. This cage is the largest of the regular rat cages
made by Martin's, and at $0.07 per square inch it provides a
lot of cage for the price. This is probably more space than
necessary for three males, but its large size lets you (a)
add more rats in the future, and (b) give the residents
enough room to play even without a lot of free range time.
But because of its size it is a bit difficult to handle,
which makes cleaning more difficult. R699 The Ruud Cage 30 x 18 x 60 Two full additional floors Four 1/3 shelves 2340 in^{2} $170 $0.07 per in^{2}  The R699 is a tower formed by placing an
R680 on top of an R695, and replacing the upper cage's
tray with a full floor. The result is two full additional
floors and four 1/3 shelves, for an inner floor space of
2340 in^{2} . This is a huge cage, standing 5 feet
tall. To make it a bit more manageable, owners suggest
attaching the top and bottom cages with temporary clips so
the cage can be broken down during cleaning. A cage of this
suze is luxurious overkill for three males. It is much loved
by rats, but its enormous size and weight make it quite
difficult to move, handle and clean.
Cages in order of least to greatest floor space:
R670 
R690 
R680 
R685 
R695 
R699 
560 in^{2} 
896 in^{2} 
900 in^{2} 
1080 in^{2} 
1440 in^{2} 
2340 in^{2} 
For those who are interested in what I ended up choosing, here was my thought process. I was looking for a cage for three male rats. For the rats' sake, I wanted the cage to be spacious, with lots of floor space. My rats don't get hours of free range time every day, so I wanted a cage they could romp around in. For my sake, I wanted a cage that had good door access, was relatively easy to handle and clean, and offered good bang for the buck. I have room for a large cage so size wasn't a constraint for me.
I chipped away at the above list. It was a tough decision, but I could only buy one cage! I eliminated the R670 as a bit small for a fulltime cage, and crossed off the R699 as being just too large to handle (alas!). Between the R680 and R685, I liked the R685's greater internal floor space and fliptop lid more than I liked the R680's big door. Between the R690 and R695, I liked the greater width, depth and floor space and gentler ramp slope of the R695, despite its increased bulk.
This narrowed the field to two cages: the R695 and the R685  the two cages with the most floor space after the Ruud cage. I loved the design of the R685: its efficient use of internal space and its flip top lid make it a good allaround cage, and a nice compromise between the rats' need to have a lot of space and the human's need to have a cage that is easy to handle, access, and clean. But I was attracted to the larger size of the R695, as my preference in cages has always been "bigger is better" (up to a point!). It was a tough call. I ended up asking Martin's if they could customize the R695 with a fliptop lid, and they could ($10 extra). This should increase access nicely. I also discovered the extra handles, which would increase the ease of handling of such a large cage. So I ended up ordering the R695, with a fliptop lid and two extra handles for easier access and handling.
The Martin's R965 I ordered arrived in a big, flat cardboard box... 
...which was stuffed with shredded newspaper: 


The cage was shipped flat, along with the tray and other accessories: 
When spread out, the parts looked like this: 


Assembly didn't take very long  maybe thirty minutes. We used cable ties instead of the metal cclips so we could break the cage back down if we needed to some day: 
Here is the assembled cage! 


The rats explore their new cage for the first time: 
With a nestbox to hide in, and hammocks to snuggle in, the rats settle in to their new home: 

