Awesome!, enjoy it its a great pair of cans. 
Well, proper amplification is quite tricky, picking up a cheap amp can ruin the sound delivery.
Sound amplification is not about getting louder, but getting clearer.
Sound is like a very detail to a tee, illustration, like a bill / note
An Amplifier is like a magnifying glass, that allow us to see all the details and very small subtleties of that illustration.
The quality of the glass will determine how well we can "Zoom in" to appreciate those details (sound dynamics, attack, speed, changes on the sound)
If this glass is dirty or scratched, opaque it wont work, that's why on audiophile we use the word "transparent" how "clean" that glass is and how well magnifies this image.
Below $100 USD you won't find a good amplifier without ruining the sound... imaging, sound-stage, all the wide airy openess the AKG has, will be ruined.
If I remember right, you can use SB X7 RCA Audio In with a Y RCA L/R to 3.5mm adapter to keep using its built-in amplifier.
Now if you are looking to make another jump and get a transparent amplifier (X7 is not) JDS Atom all the way; 5 years ago we should pay above $300 USD to get that amp transparency performance. Topping L30 or any chinese clone... I will stay away due its QC issues, there is some L30 batch out there that blows headphones.
However, there is an amazing audio british company, they make most amazing high performance-value ratio products and I guess you can find it cheaper than the rest of the world, and that is iFi Audio. iFi Zen CAN amp and you will be set, its 135 amp sounds like a an american 299 amp.
I check on amazon uk, and there is a Pro-ject 125 lb, legendary Austrian company.
So it might feelt like a little stretch but a very worthy upgrade that will unleashed all the potential of your AKG's
ifi Zen CAN > Pro-Ject > Atom
Topping L30
All those cheapo portable no-brand chinese headphone amps below $40 USD... stay away.
Hope it helps! 
Bit the bullet and bought the
iFi Zen CAN.
It works well. Sound through my 702s is now loud and clear. The addition of extra bass is very welcome and the 3D matrix works really well to take the sound outside my head. Makes a big difference to audio detection in CoD! The hiss from the X7 is still there, but no longer noticable and the interference has vanished.
My set-up:
PS4 Pro into Sound Blaster X7 via optical
PC into Sound Blaster X7 via USB
XBSX into controller via 3.5mm ext into Sound Blaster X7 via RCA adapter (line in)
Sound Blaster X7 into Zen CAN via RCA adapter (line out) (X7 volume at 100%)
Zen CAN connected to AKG K702s.
Zen CAN gain set to 12dB, volume at 40%, XBass and 3D both on.
I may just have discovered my perfect gaming audio set-up! Thanks for all your help, Alan.