`apt-get update` cannot find Ubuntu servers

It sounds like a DNS issue. To fix it, you need to ensure that

/etc/resolv.conf

has good entries for DNS servers.

Google has public DNS servers that you can use.

So for example, you could add the following 2 lines to the top of your /etc/resolv.conf file (these point at the Google DNS servers) as detailed above:

nameserver 8.8.8.8 
nameserver 8.8.4.4

Of course you'd need to be root to change this file, and make a backup before making any changes!

Can you resolve any of those hosts from the command line?

jinx:775 Z$ ping us.archive.ubuntu.com
PING us.archive.ubuntu.com (91.189.92.171) 56(84) bytes of data.
64 bytes from cassava.canonical.com (91.189.92.171): icmp_seq=1 ttl=128 time=104 ms

If not, next step is to try host -v:

jinx:776 Z$ host -v us.archive.ubuntu.com
Trying "us.archive.ubuntu.com"
;; ->>HEADER<<- opcode: QUERY, status: NOERROR, id: 14243
;; flags: qr rd ra; QUERY: 1, ANSWER: 8, AUTHORITY: 0, ADDITIONAL: 0

;; QUESTION SECTION:
;us.archive.ubuntu.com.         IN      A

;; ANSWER SECTION:
us.archive.ubuntu.com.  592     IN      A       91.189.88.31
us.archive.ubuntu.com.  592     IN      A       91.189.88.40
us.archive.ubuntu.com.  592     IN      A       91.189.88.45
us.archive.ubuntu.com.  592     IN      A       91.189.88.46
us.archive.ubuntu.com.  592     IN      A       91.189.92.169
us.archive.ubuntu.com.  592     IN      A       91.189.92.170
us.archive.ubuntu.com.  592     IN      A       91.189.92.171
us.archive.ubuntu.com.  592     IN      A       91.189.88.30

Received 167 bytes from 10.211.55.1#53 in 37 ms
Trying "us.archive.ubuntu.com"
;; ->>HEADER<<- opcode: QUERY, status: NOERROR, id: 50130
;; flags: qr rd ra; QUERY: 1, ANSWER: 0, AUTHORITY: 1, ADDITIONAL: 0

;; QUESTION SECTION:
;us.archive.ubuntu.com.         IN      AAAA

;; AUTHORITY SECTION:
ubuntu.com.             1800    IN      SOA     ns1.canonical.com. hostmaster.canonical.com. 2011030301 10800 3600 604800 3600

Received 100 bytes from 10.211.55.1#53 in 65 ms
Trying "us.archive.ubuntu.com"
;; ->>HEADER<<- opcode: QUERY, status: NOERROR, id: 54875
;; flags: qr rd ra; QUERY: 1, ANSWER: 0, AUTHORITY: 1, ADDITIONAL: 0

;; QUESTION SECTION:
;us.archive.ubuntu.com.         IN      MX

;; AUTHORITY SECTION:
ubuntu.com.             1800    IN      SOA     ns1.canonical.com. hostmaster.canonical.com. 2011030301 10800 3600 604800 3600

Received 100 bytes from 10.211.55.1#53 in 62 ms

Look for errors returned by DNS servers.

I know this thread is super old, but for anyone still looking on, I solved this problem by disconnecting and reconnecting to wireless access point.