TM4C123G maximum current extraction through GPIO

8mA I believe is the best you can do and stay in the voltage levels of connected "standard" 3.3V logic.

Absolute max is 25mA per pin (your now outside those standard logic levels)

Also a useful note in "recommended operating conditions" 

Recommended Operating Conditions
For special high-current applications, the GPIO output buffers may be used with the following
restrictions. With the GPIO pins configured as 8-mA output drivers, a total of four GPIO outputs may
be used to sink current loads up to 18 mA each. At 18-mA sink current loading, the VOL value is
specified as 1.2 V. The high-current GPIO package pins must be selected such that there are only
a maximum of two per side of the physical package with the total number of high-current GPIO
outputs not exceeding four for the entire package.

In the datasheet it's indicated that  it's 12mA, there are some pads that suport 18mA.

Luis - thanks for that.

Identifying that MCU manual by part name - it's Rev & Date - and the page which supports your findings would prove even more helpful/useful...  (beware that you've not provided "absolute max ratings"...)

Absent your written findings - my read of our MCU manual agrees with data supplied earlier by friend Dexter...

As to poster's (unspoken) intent - it is classically "unwise" to employ any MCU as, "beast of burden."  Small, multi-channel signal buffers exist - exactly targeting such usage.  Your design may often benefit from a simple, pin-programmable "logic gate" - (this vendor provides) which provides boosted current output and may reduce software complexity as well...

To note this, this is from the datasheet of the tm4c1294ncpdt but it should be taken into consideration for i/o realibility

I/O Reliability
For typical continuous drive applications, I/O pins configured between 2 mA and 12 mA and operating
at -40 to 85°C, meet the standard 10-year lifetime reliability. If a continuous current sink of 18 mA
is required, then operation is limited to 0 to 75°C in order to meet the standard 10-year reliability.
At 105°C, I/O configured for continuous drive meet the standard 2.5 year lifetime reliability.
In typical switching applications (40% switch rate) operating at -40 to 85°C, all I/O configurations
except 2 mA meet the standard 10-year lifetime reliability with 50-pF loading. By limiting the capacitive
loading to 20 pF for an I/O configured to 2 mA, the 10-year lifetime reliability can be met at -40 to
85°C.
In typical switching applications (40% switch rate) operating at 105°C, all I/O configurations except
2 mA meet the standard 2.5-year lifetime reliability. By reducing the capacitive loading to 20 pF with
a typical switching rate at 105°C, a 2-mA I/O configuration meets a 2.5 year lifetime reliability.
April 22, 2014 1831
Texas Instruments-

Now from the tm4c123gh6pm. Altough there are those recomended currents for each pin, there's also a limit in cumulatibe GPIO:

The sides are descrived here:

The post's title, "Maximum current extraction thru gpio" by itself troubles - raises flags.  Through several decades of successful, ramping MCU use - we've long learned that it is unwise to employ the MCU as, "beast of burden."  Other parts far better manage that task - and done improperly or w/out great care/detail - the MCU may be damaged!

Here the, "Recommended GPIO Pad Operating Conditions" for poster's TM4C (not 129x) (more mainstream device):

And - this is exactly as poster Dexter reported - he being a past, valued vendor MCU engineer - very active here.

As my post detailed - there are other - safer & preferred means - to "extract current."  I stand by those comments...