SSH Tunnel Timing out on client side - ssh

Question

So I'm on my local machine, and I'm sshing into a google compute server.
From this google compute server, I'm trying to establish an ssh tunnel to a third party server ($host) using the following command:
ssh username#$host -L 3306:127.0.0.1:3306 -N
And after hanging for 20-30 seconds, I get:
ssh: connect to host $host port 22: Connection timed out
I can use the exact same command on my local machinet to the third party server and it works fine.
I've killed anything using the 3306 port on the google compute server.
I've opened port 22 and 3306 on the google server through the interface (through I can't tell if this applies to outbound connections also).
Not sure where to go from here, any help would be appreciated.
Edit1: The google server can successfully ping the third party server.
Edit2: Just tried it from the company server, it doesn't work there either. Both he google-compute and the company server are linux (Deb Wee and Ubuntu respectively) and the local machine is windows. The fact that I'm sshing into them shouldn't make a difference should it?
Edit3: Changed the default SSH port on the google server to 22222 and connected to it using that instead. Trying to connect to third party now with:
sudo ssh -p 22 username#$host -L 3306:127.0.0.1:3306 -N -v -v -v
Debug output is:
OpenSSH_6.6.1, OpenSSL 1.0.1e 11 Feb 2013
debug1: Reading configuration data /etc/ssh/ssh_config
debug1: /etc/ssh/ssh_config line 19: Applying options for *
debug2: ssh_connect: needpriv 0
debug1: Connecting to $host [$host] port 22.
And after that it just hangs.
Debug output on local machine using same command is is:
OpenSSH_4.6p1, OpenSSL 0.9.8e 23 Feb 2007
debug2: ssh_connect: needpriv 0
debug1: Connecting to $host [$host] port 22.
debug1: Connection established.
*other junk*

Answer 1

Turns out the third party server had ssh blocked from anywhere outside Australia
-_-