It is generally better to build your own desktop-tower PC or buy a semi-custom pre-built than gamble on a branded PC when thinking upgrade potential. These questions involve searching forums for discussion and evaluating what was said and what was actually done. This generally takes a knowledgeable person physically looking at exactly what you have now.
Your motherboard size and mounting pin locations are micro-atx and the motherboard should fit in any case that accepts micro-atx boards. There are a few noted upgrade issues.
The main power connection from the power supply to the motherboard is a special 14 pin instead of a 24 pin.
To change the power supply, you need to buy or create an adaptor or customized cable. A 24 to 14 pin cable for the H50 has been offered on ebay and at amazon in the past and may still be available. A method to do it yourself is shown on youtube.
The GTX 950 was not in the Lenovo standard offerings.
There were several versions of GTX 950 and one was/is a 75 watt that does not require a pcie 6 pin connection from the power supply, but standard ones do require it. If you have a standard GTX 950, somebody upgraded the power supply already, or rigged in a molex to PCIe 6 pin adaptor cable for an insufficient power supply. This needs to be determined to understand what you are starting with.
In moving to a different usually larger computer case, the key issues are about connecting the front panel electronics. The power button, USB, audio, fans may or may not have standard connections.
USB probably yes as standard. Power button cable as a maybe, and would be great to look at your motherboard versus the standard in a new case. Fan headers are probably missing from the motherboard and require direct connection to 12 volts at the power supply. A fan controller could have the same issue.
To keep your computer case, you cannot use long graphics cards without moving the hard drive storage.
Your case cooling air flow issue, if you have one, can be resolved by matching your system fan size and changing to a much stronger fan. PCPARTPICKER.COM is a useful site for shopping and compatibility.
Most cube cases are for itx size motherboards.
not a cube, but purple led and cheap in the usa. Providing your country is important for shopping and availability, and your Zotac GTX 950 indicates non-USA.
You can usually swap out case fans easily, and the Fractal Design Focus G mini is a nice case
Apevia X-Qpack3 comes in a variety of color
Fancy expensive cases are available
But you cannot use a case that only accepts ITX boards, and typically it is the power supply that needs upgrade.