Ubuntu show wrong disk sizes, how to solve it?

It looks like that you have made raid1 (mirror) between partitions on your SSD and HDD. This is not best practice, since it more or less restricts performance to that of the slowest disk.

You can see that /boot, / and [ SWAP ] is defined on partitions on both /dev/sda and /dev/sdb.

sdb       8:16   1 238.4G  0 disk
├─sdb2    8:18   1   512M  0 part
│ └─md1   9:1    0 511.4M  0 raid1 /boot
├─sdb3    8:19   1 229.9G  0 part
│ └─md2   9:2    0 229.8G  0 raid1 /
└─sdb1    8:17   1     8G  0 part
  └─md0   9:0    0     8G  0 raid1 [SWAP]
sda       8:0    1   2.7T  0 disk
├─sda2    8:2    1   512M  0 part
│ └─md1   9:1    0 511.4M  0 raid1 /boot
├─sda3    8:3    1 229.9G  0 part
│ └─md2   9:2    0 229.8G  0 raid1 /
└─sda1    8:1    1     8G  0 part
  └─md0   9:0    0     8G  0 raid1 [SWAP]

I would recommend that you reinstall Ubuntu using only SSD for /boot, / and SWAP. If yopu really want a raid1/mirror setup, you should buy one more 240 GB SSD, so you mirror between similar type and size disks.

Anyway .. if you take a look at your disks with gparted (or fdisk -l) you should see a huge unallocated amount of data on /dev/sda.

The reason why your "3,0 TB" drive (sda) shows up as 2.7T is most likely due to different units being used.

The size is probably about 2.7 Tebibyte, which is approximately the same as 3.0 TB.

You can read about it here: https://en.wikipedia.org/wiki/Tebibyte

lsblk shows all disk partitions, while df -lh only shows your mounted partitions.