unable to install g++ and build-essentials in ubuntu 20.04

TL;DR: had to downgrade libc6 and then was able to install build-essential

Experienced the same thing:

$ sudo apt install build-essential
Reading package lists... Done
Building dependency tree
Reading state information... Done
Some packages could not be installed. This may mean that you have
requested an impossible situation or if you are using the unstable
distribution that some required packages have not yet been created
or been moved out of Incoming.
The following information may help to resolve the situation:

The following packages have unmet dependencies:
 build-essential : Depends: libc6-dev but it is not going to be installed or
                            libc-dev
                   Depends: g++ (>= 4:9.2) but it is not going to be installed
E: Unable to correct problems, you have held broken packages.

Here's what I did to fix it.

Checked apt-cache policy g++, I thought this was already satisfied so I moved on:

$ apt-cache policy g++
g++:
  Installed: (none)
  Candidate: 4:9.3.0-1ubuntu2
  Version table:
     4:9.3.0-1ubuntu2 500
        500 http://mirrors.xtom.com/ubuntu focal/main amd64 Packages

Checked apt-cache policy libc6-dev:

$ apt-cache policy libc6-dev
libc6-dev:
  Installed: (none)
  Candidate: 2.31-0ubuntu9.2
  Version table:
     2.31-0ubuntu9.2 500
        500 http://mirrors.xtom.com/ubuntu focal-updates/main amd64 Packages
     2.31-0ubuntu9 500
        500 http://mirrors.xtom.com/ubuntu focal/main amd64 Packages

Tried to install a specific version (the latest shown above):

$ sudo apt install libc6-dev=2.31-0ubuntu9.2
Reading package lists... Done
Building dependency tree
Reading state information... Done
Some packages could not be installed. This may mean that you have
requested an impossible situation or if you are using the unstable
distribution that some required packages have not yet been created
or been moved out of Incoming.
The following information may help to resolve the situation:

The following packages have unmet dependencies:
 libc6-dev : Depends: libc6 (= 2.31-0ubuntu9.2) but 2.31-0ubuntu9.3 is to be installed
E: Unable to correct problems, you have held broken packages.

Did the same thing, tried to install that specific libc6 version:

$ sudo apt install libc6=2.31-0ubuntu9.2
Reading package lists... Done
Building dependency tree
Reading state information... Done
Suggested packages:
  glibc-doc
The following packages will be DOWNGRADED:
  libc6
0 upgraded, 0 newly installed, 1 downgraded, 0 to remove and 0 not upgraded.
Need to get 2,715 kB of archives.
After this operation, 0 B of additional disk space will be used.
Do you want to continue? [Y/n]
...
dpkg: warning: downgrading libc6:amd64 from 2.31-0ubuntu9.3 to 2.31-0ubuntu9.2
...

Emphasis on the warning I got: dpkg: warning: downgrading libc6:amd64 from 2.31-0ubuntu9.3 to 2.31-0ubuntu9.2

Now I was able to install build-essential:

$ sudo apt install build-essential
Reading package lists... Done
Building dependency tree
Reading state information... Done
The following additional packages will be installed:
  g++ g++-9 libc-dev-bin libc6-dev libcrypt-dev libstdc++-9-dev linux-libc-dev manpages-dev
Suggested packages:
  g++-multilib g++-9-multilib gcc-9-doc glibc-doc libstdc++-9-doc
The following NEW packages will be installed:
  build-essential g++ g++-9 libc-dev-bin libc6-dev libcrypt-dev libstdc++-9-dev linux-libc-dev manpages-dev
0 upgraded, 9 newly installed, 0 to remove and 0 not upgraded.
Need to get 16.2 MB of archives.
After this operation, 77.1 MB of additional disk space will be used.
Do you want to continue? [Y/n]

I read multiple different stackoverflow posts that led me to use the apt-cache policy $package that I was not familiar with. Then I just played around.

After looking for an answer, I figured to manually install the "correct" version manually, and came across this when downloading the pkg file:

Add the following line to /etc/apt/sources.list:

deb http://archive.ubuntu.com/ubuntu/ focal-proposed main

Update the package index:

sudo apt-get update

After adding this repository, I was able to install build-essential with the command:

sudo apt-get install build-essential

I suppose I found a super simple solution by chance. No downgrade or kernel builds. Just ran

sudo apt update && sudo apt upgrade -y

There were 3 repositories returning errors in my case. Such as,

E: The repository 'cdrom://Ubuntu 20.04 LTS _Focal Fossa_ - Release amd64 (20200423) focal Release' does not have a Release file.

Just launched software updater, removed PPAs with errors, now I'm able to install new software without getting

Depends: libc6 (>= 2.33) but 2.31-0ubuntu9.2 is to be installed

error.

You have to apply for support of 'Canonical Partners' from Software & Updates.

Software & Updates of Ubuntu20

Mark 'tick' in Canonical Partners (not the source code one) and then do

sudo apt install build-essential